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For the crust:
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Preheat oven to 300 F. Lightly spray a 9-inch springform pan with non-stick cooking spray. Line the bottom of the pan with parchment paper and lightly spray parchment and sides of pan with non-stick spray.
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Place cookies in the bowl of a food processor and process to very fine crumbs. You should have about 3 1/2 cups. Transfer to a small bowl. Add melted butter and, using a spatula, stir until well combined.
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Pour crumb mixture into prepared pan and press evenly with the back of a spoon into bottom and up sides of the pan, leaving about 1/2 inch between the top of the crust and top of the pan. Transfer to freezer until crust is set, about 10 minutes.
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Transfer crust to oven and bake until dry to the touch, about 10 minutes. Transfer pan to a wire rack and let cool.
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For the Flourless Red Velvet Cake:
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Increase oven temperature to 350 F.
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Place butter and chocolate in a microwave safe bowl and heat in the microwave for about 30-45 seconds until chocolate is melted. Stir chocolate and butter together until blended. If it's not melted yet, continue to heat for 30 seconds at a time.
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In a small bowl, whisk together salt, red food coloring, vinegar and vanilla; set aside.
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In the bowl of an electric mixer fitted with the whisk attachment, beat egg yolks with 1/2 cup sugar until light and almost doubled in volume, about 5 minutes. Add melted chocolate and butter mixture and beat until just combined. Scrape down sides and bottom of the bowl and mix on low speed for 5 seconds. Add red food coloring mixture and beat until just combined. Scrape down the sides and bottom of the bowl and mix on low for 5 seconds. Set aside.
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Using another clean bowl and the electric mixer fitted with the whisk attachment, beat egg whites until foamy. Gradually increase speed to high and slowly add remaining 1/4 cup sugar, beating until soft peaks form.
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Transfer 1 cup of the egg white mixture to the chocolate mixture and, using a rubber spatula, gently fold to combine, about 30 seconds. Add remaining egg whites and continue gently folding until they are almost completely combined; do not over-mix.
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Pour into the cooled cookie crust, smooth the top and transfer to the oven. Bake until cake is set but still jiggles slightly, 38 to 42 minutes. It may not appear completely cooked at this point but press on. Transfer to a wire rack to cool completely still in the pan. Cake will deflate in the center as it cools.
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Tightly wrap cooled cake (still in the pan) with plastic wrap and refrigerate at least 3 hours or place in the freezer for 1 1/2 hours.
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For the Red Velvet Pudding:
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In a medium saucepan, whisk together sugar, cocoa powder, cornstarch, and salt. Add egg yolks and whisk until combined. The mixture will look like a thick paste. Slowly pour in milk and buttermilk and whisk until well incorporated.
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Place saucepan over medium heat and bring mixture to a boil, whisking constantly to prevent it from burning on the bottom of the pan. Boil for 45 seconds-1 minute and immediately transfer to a medium bowl.
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Add butter, vanilla and red food coloring; whisk until combined. Continue whisking until mixture is cooled slightly. Let stand at room temperature for 15 minutes. Press a piece of plastic wrap directly on the surface of pudding to prevent a skin from forming. Transfer to the refrigerator until chilled, at least 3 hours or place in freezer for 1 1/2 hours.
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When ready to assemble, stir pudding to loosen it and pour it on top of cake, making sure to stay within the cookie crust border. Using an offset spatula, spread pudding to form an even layer on top of the cake. Transfer to the refrigerator for 30 minutes. During this time, chill the bowl and whisk attachment of your electric mixer by putting them in the freezer.
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For the cream cheese whipped cream topping:
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In the chilled bowl of an electric mixer fitted with a chilled whisk attachment, beat cream cheese, sugar and vanilla extract on high. Slowly add in whipped cream and whip until stiff peaks form. Spread whipped cream over chilled pudding layer, working all the way out to the sides.
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Unmold cake and serve immediately. The cake can also be kept, covered, refrigerated, for up to 2 days.
