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Make the Chocolate Cookie Crust: Preheat oven to 300 degrees.
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2
Lightly spray a 9-inch springform pan with nonstick cooking spray.
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Line pan with parchment paper and lightly spray parchment and sides of pan.
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4
Place cookies in the bowl of a food processor; process to very fine crumbs.
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You should have about 3 1/2 cups.
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Transfer to a small bowl.
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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, leaving about 1/2 inch between the top of the crust and top of the pan.
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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.
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Transfer pan to a wire rack and let cool.
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12
Make the Flourless Chocolate Cake: Increase oven temperature to 350 degrees.
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13
Place butter and chocolate in a heatproof bowl set over (but not touching) simmering water to melt; stir to combine.
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14
Remove from heat.
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15
In a small bowl, whisk together espresso powder, coffee, salt, 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.
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Add melted chocolate mixture and beat until just combined.
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Scrape down sides and bottom of the bowl and mix on low speed for 5 seconds.
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Add coffee mixture and beat until just combined.
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Scrape down the sides and bottom of the bowl and mix on low for 5 seconds.
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In the clean bowl of an electric mixer fitted with the whisk attachment, beat egg whites until foamy.
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Gradually increase speed to high and slowly add remaining 1/2 cup sugar, beating until soft peaks form.
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Transfer 1 cup egg white mixture to chocolate mixture and, using a rubber spatula, gently fold to combine, about 30 seconds.
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Add remaining egg whites and continue gently folding until they are almost completely combined; do not overmix.
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Pour into cooled cookie crust and transfer to oven.
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Bake until cake is set but still jiggles slightly, 38 to 42 minutes.
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It may not appear completely cooked.
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Transfer to a wire rack to cool completely.
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Cake will deflate in the center as it cools.
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Tightly wrap cooled cake with plastic wrap and refrigerate at least 3 hours and up to overnight.
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Make the Chocolate Pudding: In a medium saucepan, whisk together sugar, cocoa powder, cornstarch, and salt.
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Add egg yolks and whisk until combined.
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The mixture will look like a thick paste.
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Slowly pour in milk, whisking constantly.
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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.
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Boil for 30 seconds and immediately transfer to a medium bowl.
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Add butter, vanilla, and chocolate; whisk until combined.
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Continue whisking until mixture is cooled slightly.
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Let stand at room temperature for 15 minutes.
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Press a piece of plastic wrap directly on the surface of pudding to prevent a skin from forming.
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Transfer to refrigerator until chilled, at least 3 hours.
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42
Stir pudding to loosen and pour on top of cake, making sure to stay within the cookie crust border.
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Using an offset spatula, spread pudding to form an even layer on top of the cake.
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Transfer to refrigerator for 30 minutes.
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45
Prepare the Whipped Cream Topping: In the chilled bowl of an electric mixer fitted with a chilled whisk attachment, beat cream until soft peaks form, about 1 minute.
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Sprinkle sugar over cream and continue whisking until stiff peaks form.
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Spread whipped cream over chilled pudding layer, working all the way out to the sides.
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Unmold cake and serve immediately.
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The cake can also be kept, covered, refrigerated, for up to 2 days.