This rich, silky cheesecake has a nutty graham cracker crust and a brûléed top, which adds a delightful caramelized crunch. (Plan ahead: Crust and cheesecake are baked separately and assembled afterward to keep the crust crisp.)
Make brown butter: In a small saucepan, melt the butter over medium-low heat. Cook until the milk solids separate out and the butter turns deeply golden and fragrant like toasted nuts, 10 minutes. Refrigerate until solid, 15 minutes. You should have 4 ounces of brown butter. Meanwhile, pulse and grind the graham crackers to fine crumbs in a food processor. Measure out ¾ cup (81 g) of crumbs and set aside.
Graham Cracker Crust: Add the brown butter to the bowl of a stand mixer fitted with a paddle attachment. Mix on low speed to soften, 30 seconds, then add the brown sugar and continue mixing on medium speed, 2 minutes. Scrape down the bowl. Crack the egg into a small cup or bowl and add the vanilla. With the mixer running on medium speed, add the egg and vanilla to the batter and mix to combine almost all the way. Turn the mixer off; scrape the sides and bottom of the bowl with a rubber spatula to bring the batter together. Mix on medium speed for 30 seconds until nearly homogeneous; turn mixer off. Add both flours, both salts, and graham cracker crumbs; mix on low speed until the dough just comes together but still looks shaggy, about 30 seconds. Do not overmix. Remove the bowl from the stand mixer; use a plastic bench scraper to transfer the dough to a work surface. Bring the dough together into a disk. Wrap disk in plastic wrap and refrigerate until chilled throughout, 1 hour or up to overnight. (Keeps for up to two days in the refrigerator.)
Bring dough to room temperature, 10 minutes. Meanwhile, preheat oven to 325 F. Trace the circumference of a 10-inch springform pan onto parchment paper: this will be the template for rolling the dough into a circle. Spray your work surface with nonstick spray and lay the prepared parchment paper on it; the spray will keep the parchment from slipping as you work. Knead dough several times and shape into a ball. Using your hands and the rolling pin, flatten the dough into a thick disk. Dust the parchment with flour, then place the dough on it; dust the dough with flour. Using short strokes of the rolling pin, flatten the disk to be 1 inch larger than the circle, all the way around. (If the dough cracks, pinch it back together.) Place the plate of the springform pan over the circle and use a knife to trim the edges so the crust is flush with the plate. (Save extra dough for another use, such as making cookies.) Remove the plate, cover the dough with another sheet of parchment paper, flip over; then peel off and set aside the top layer of parchment. Make sure there’s no residual flour on top; if there is, gently brush it off. Place the dough on a rimmed baking sheet and bake until golden, about 15 minutes.
Crust is ready when it is golden brown and feels like a cookie. Remove from oven and let cool completely on a wire rack, either at room temperature or in the refrigerator. (Crust can be made 1 day ahead and stored at room temperature or in the refrigerator, lightly covered.)
Cheesecake: Preheat oven to 300 F. Add cream cheese to the bowl of a stand mixer fitted with a paddle attachment. Mix on low speed and blend until smooth, 1–2 minutes. Add sugar and continue mixing on medium speed until aerated, 2 minutes. Meanwhile, prepare the springform pan: Grease the inside with nonstick spray, then line the plate with a fitted parchment circle. Spray again. Wrap the outer sides and bottom of the pan with foil to insure there is no leakage. Set aside.Once the cream cheese mixture is fully aerated, scrape the sides and bottom of the bowl to bring the mixture together. Crack the eggs into a small bowl and add the vanilla.
With the mixer on medium speed, add one egg at a time to the cream cheese mixture. When just incorporated, turn off the mixer and scrape down the sides and bottom of the bowl. Add sour cream, heavy cream, and salt; mix on low speed just to incorporate. Place a fine-mesh strainer over a large bowl and pour the cheesecake mixture through, using a rubber spatula to pass it into the bowl. Pour the strained mixture into the prepared pan. Use a spatula to smooth the top; give the pan a few light taps on the countertop to remove air bubbles. Place the pan into a large roasting pan and then into the oven. Pour enough water into the roasting pan to go halfway to the level of the cheesecake filling. Bake 40–45 minutes, checking after 30 minutes. Cheesecake is done when it feels set when poked gently. Remove pan to a towel to dry the bottom. Place in the freezer for at least 1 hour, or up to overnight.
Assembly: Remove springform ring from frozen cheesecake. Stack crust on top of cheesecake, then invert onto a baking sheet so the springform plate is on top. Gently remove plate and peel off the parchment paper. Brûlée Topping (optional): Distribute a thin, even layer of superfine sugar on top of the cheesecake. Move a torch across the top until the sugar bubbles and caramelizes. Allow the cheesecake to rest until the sugar hardens. (You may serve it without the brûléed top, or add a berry garnish.)