This story begins at a party. I’m sitting on the floor, trying to negotiate a shipment of venison liver from my friend Karen. Her neighbor is an avid bowhunter, and a great dessert-lover. Karen has devoured a chunk of my Root Beer Float cheesecake and thinks a swap might be do-able. I’ve never had venison liver but I would love to try.
Which is when our mutual friend Rachel enters the conversation. “You’re talking cheesecake ... again,” Rachel avers, as we nod, smiling.
“Do you have to use a springform pan?” she asks.
Without thinking, I quickly say, “Yes.”
“Oh, that’s too bad,” she answers. “I only ever see them big.”
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| Selection of pie pans: 9" (left) 6" (silver) and 4" (gunmetal gray) |
It’s true - in most houseware stores, the only springform pan you’re likely to see is 9” across. Fill this puppy all the way to its top with cheesecake and you’ve got at least 12 huge servings. Of course you can make a half-recipe, with its resulting not-very-high cheesecake, but still you end up with massive plates of sweet.
“Yeah, that’s a problem,” I agree. “But, look what I found at a farm market last year.” I swoop into a storage drawer and come up with a 4” springform pan.
“Cute!” Rachel says. But then, before I can riff on the virtues of 4” cheesecakes, someone interrupts and the conversation fragments.
What I might have said, had Rachel or Karen questioned me, was that a 4” cheesecake was just about perfect for a couple or small family, but that an intuitive baker would make a grand mistake scaling his recipes for it. That would be because, while the 4” pan seems to be about 1/2 the size of a 9” pan, it is actually much, much smaller.
And, yes, this post is about math.
Baked goods are three-dimensional; therefore, they have volume. To scale a recipe up or down, we must sometimes perform calculations.
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| Spring form pans - 9" and 4" |
Consider a simple rectangular cake. A recipe might say, “Grease a 9” square cake pan,” but what it really means is, “Grease a 9” X 9” X 2” pan.” The extra dimension is crucial for anyone who wants to convert the recipe to circular pans or larger, or smaller rectangles. Conversion requires knowing volume, and volume must be calculated by the following: (Area) X (Height.) In this case, the pan area is (9)2 but the volume is (9)2 X 2, or 162 cubic inches.
Were you to reach into the cupboard and pull out an 8” pan by mistake, the overflow would not be small, for an 8 X 8 X 2 pan has a volume of 128 cubic inches. 34 cubic inches of overflow on your counter is nothing to sneeze at, and it represents a lot of sponge-mopping, a lot of waste.
Most of us can perform such simple math, but the situation gets slippery when circles, triangles, and weird shapes are involved. The volume of a column - which is what we have with circular baking pans - is calculated as πr2 X h, with π = 3.1417, r = the radius of the circular base and h = the height of the column. A 9” baking pan has a diameter of 9”, thus a radius of 4.5”. If its height is 2”, its volume is 127.2 cubic inches - or even less than the 8 X 8 X 2 rectangular pan.
Now I have some ‘splaining to do. I’ve been harping on the advantages of weighing ingredients for so long it may seem like I’m backtracking to suggest that volumes are useful. However, understanding how to determine and proportion volume does not negate the superiority of measuring by weight. No matter how you measure baking ingredients, you’d need an engineers worth of math to anticipate the actual liquid volume of ingredients when combined. So when I set out to make a micro-dessert, and my point of departure is a standard, feed-a-farm-family recipe, I check the pan size in the recipe first, then scale ingredients - using percentages - based on the pan I’ll be using.
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| The "Cute" pan - 4" springform |
This is where weight measurements come in handy. Reducing a weight measurement by a percentage is child’s play, but try it with volumes.
For example: a 9” round cheesecake recipe calls for 4 tablespoons of toasted almond flour, which weighs 12 grams per tablespoon (48 grams.) I want to make a 4” round cheesecake. How much almond flour do I use?
(Shortcut answer: Who the hell cares? A tablespoon and a half is close enough! A little bit of almond flour one way or the other hardly matters!) {But would anybody’s grandmother accept that? Not in a family of educators and scientists .... Like mine}
Anyway - the volume of my 3” deep, 4” diameter cheesecake pan is 38 cubic inches, about 30% of the volume of the 9” pan. 4 TBLSP X .30 = 1.2, or a tablespoon-and-a-quarter, more or less. Using weight, 48 grams X .3 = 14.4 grams.
Who’s even seen a quarter-tablespoon measuring device? But 14 grams on a cheap cook scale is totally easy - and if you have a Cole Palmer home science scale that measures tenth of grams (I do, natch) you can be totally accurate. Which means your cheesecakes will be consistent - a good thing.
But now you’re sick of numbers and want a recipe. So here it is, my famous Root Beer Float cheesecake (Mostly borrowed from America’s Test Kitchen Family Baking Book). Oh, but wait - this is as much a quiz as it is a recipe. What follows is a recipe for a 9” diameter, 2.75” deep springform pan. If you want to adapt it to a smaller (or, God forbid, larger) size, you’ll need to do the math yourself!
NOTE: Although I use pieces of wild sassafras root bark in this recipe, several sources caution that genuine sassafras may have carcinogenic properties. I am unable to verify or disprove this, so if the prospect frightens you, use an alternative to sassafras root, such as sassafras oil (Click HERE), substituting 1/2 tsp sassafras oil for the ingredients I list below. If on the other hand, you are like my father, who waved a hand in nonchalance over his daily cup of sassafras tea when I told him the carcinogenic news, and then went on to live to 95, perhaps you should come sassafras foraging with me this March. That’s probably the only way you’ll get real sassafras root.
Root Beer Float Cheesecake
Serves 12 - 20
For the crust:
100 grams (+/-) dried, crumbled GF cookies or dry, leftover GF cake
40 grams almond flour or almonds processed in a food processor to fine consistency
3/4 stick unsalted butter softened to room temperature, plus @ 1 TBLS for greasing the pan
3 TBLSP granulated sugar
For the filling:
2.5 lbs cream cheese (do NOT use “lite” or “reduced fat” cream cheese) softened at room temperature.
1.5 oz sugar
1/8 tsp salt
1/3 cup sour cream (I prefer Daisy brand as it is the only one made from cream and nothing but. How can you call something sour cream when it includes skim milk???)
6 large eggs
2 large egg yolks
2 TBLSP heavy cream
1 TBLSP vodka, brandy, or water
@ 2 grams sassafras root-bark, peeled and dried
For the topping:
4 oz heavy whipping cream
1/2 tsp vanilla extract
Instructions:
Place 2 TBLSP of heavy cream in a small bowl and drop 1/2 the sassafras in it. Stir until sassafras is covered, then cover bowl with plastic wrap and set aside at room temperature for at least 6 hours, or overnight.
In a mortar and pestle, pound the remaining sassafras root bark to a fine powder. Add the vodka, brandy or water to this and allow to steep at least one hour.
Thoroughly grease the bottom of a 9” springform pan. Cut a circle of baker’s parchment and place it in the pan bottom. Preheat oven to 325 F.
Place the cookies, almond flour and sugar in a food processor. Pulse to a coarse meal. Add butter and pulse until dough comes together. Spread this on the bottom of the pan, taking care to make an even, flat layer. Bake @ 15 minutes, or until the crust just begins to brown. Remove from the oven and allow to cool.
Increase oven temperature to 500 F. Cut the cream cheese into small chunks and add them one at a time to a stand mixer, equipped with a paddle blade, running at medium low speed. Beat 1 - 3 minutes or until very smooth. Beat in sugar and salt, half at a time, until incorporated. Beat in the sour cream until incorporated.
Remove sassafras bark from the heavy cream and add the cream to the mix, beating until incorporated. Add the vodka/brandy/water extract and beat. Beat in the egg yolks and eggs two at a time and beat 1 - 3 minutes, until very smooth.
Brush the walls of the springform pan with melted butter. Wrap a ring of aluminum foil around the outside of the pan. Place pan on baking sheet, pour filling into pan, and place into the oven. Bake for 10 minutes, then reduce heat to 200 F without opening oven door. After 45 minutes rotate pan 180 degrees and check inner temperature. In another 30 minutes check temperature again. You want the cheesecake to be 150 F.
Before removing cake from the oven, run a knife around the inner edge of the pan. Turn heat off and allow pan to remain in oven 5 minutes. Remove to a cooling rack. After 10 minutes run the knife around the inside again, and do so periodically as the cake slowly cools to room temperature.
When cake reaches room temperature, cover with plastic wrap and refrigerate.
When cake is cold, remove from refrigerator, release springform edge and carefully remove the cake from the pan. Slide cake from springform bottom onto plastic or wooden serving tray (so that you will not dull your knife as you slice pieces), retaining the parchment. (If you are able to carefully peel off the parchment, do so. However it may be easier to remove parchment individually from slices.)
Whip the heavy cream and vanilla to make a frosting. Spread atop cake. Cut with a clean, wet knife, washing the knife between each slice. Enjoy!
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