1. Make the filling: In the bowl of an electric mixer, combine chocolate and salt; set aside. Place 1 tablespoon heavy cream in a small bowl; sprinkle gelatin over cream and let stand until softened, about 10 minutes.

2. Meanwhile, place remaining 3/4 cup plus 3 tablespoons heavy cream and 1 tablespoon sugar in a small saucepan and bring to a simmer over medium heat, stirring, until sugar has dissolved. In a medium bowl, whisk together egg yolks and remaining tablespoon sugar. Gradually whisk hot cream mixture into egg mixture. Return cream mixture to saucepan and place over medium heat; cook, whisking constantly, until mixture is thickened and coats the back of a spoon, about 3 minutes. Remove from heat.

3. Stir gelatin mixture into cream mixture. Strain gelatin mixture into bowl with chocolate mixture; let stand 1 minute. Whisk until chocolate is melted and smooth. Whisk in creme fraiche. Attach bowl to electric mixer fitted with the whisk attachment and beat filling until well combined, about 2 minutes. Cover with plastic wrap, pressing down on the surface of the filling to prevent a skin from forming. Transfer to refrigerator and let chill overnight.

4. Make the cake: Preheat oven to 350 degrees. Spray the bottom and sides of three 9-inch round cake pans with cooking spray. Line bottom of pans with parchment-paper rounds; set aside.

5. Sift cocoa powder into a medium bowl; whisk in egg and egg white. Gradually whisk in 1/4 cup plus 2 tablespoons lukewarm water; continue whisking until smooth. Set aside. In another medium bowl, whisk together both flours, baking soda and baking powder; set aside.

6. In the bowl of an electric mixer fitted with the paddle attachment, beat together brown sugar, butter, vanilla, and salt, until smooth, about 2 minutes, scraping down the sides of the bowl as necessary. Gradually beat cocoa mixture into butter mixture. Add flour mixture in three additions, alternating with buttermilk, and mixing well after each addition. Fold in cocoa nibs and ground espresso.

7. Divide batter evenly among prepared cake pans; smooth tops. Transfer to oven and bake until a cake tester inserted into the center of each comes out clean, about 17 minutes. Transfer pans to wire rack and let cool completely before inverting cakes onto wire racks. At this point, cakes can be wrapped individually in plastic wrap and kept at room temperature for up to 1 day. Transfer cake layers to freezer; freeze until firm before frosting.

8. Assemble: Place Chocolate Crumb Base on a cake plate; using an adjustable cake ring as a guide, top with 1 layer of cake. Stir filling to loosen and spread half (about 1 cup) over layer; top with a second layer, followed by remaining filling. Top with remaining layer of cake. Transfer to refrigerator and let chill for 1 hour.

9. Spoon icing over top of cake; smooth over top and sides, swirling decoratively. If desired, use a kitchen torch to brulee frosting in several spots. Cake can be served immediately or covered with a cake dome and kept chilled for up to 1 day; let stand at room temperature for 1 hour before serving.