Ingredients
Cake

Filling

Glaze

Methods

For cake:
Position rack in center of oven and preheat to 375°F. Lightly butter two 9-inch-diameter cake pans with 1 1/2-inch-high sides. Line bottom of pans with parchment paper. Combine chocolate and 2 tablespoons water in top of double boiler set over simmering water. Stir until chocolate is smooth. Remove from over water. Transfer chocolate to large bowl; cool 5 minutes. Whisk egg yolks into chocolate. Beat whites in medium bowl until soft peaks form. Add sugar 1 tablespoon at a time, beating until stiff and glossy. Fold 1/4 of whites into chocolate to lighten. Gently fold in remaining whites in 2 additions just until combined and being careful not to deflate batter.

Divide batter between prepared pans (layers will be very thin). Bake until cakes begin to pull away from sides of pans and tester inserted into center comes out clean, about 10 minutes. Cool cakes in pans on rack 1 hour. Carefully invert cakes onto 9-inch-diameter cardboard rounds or tart pan bottoms. Cool cakes completely. Peel off parchment paper.

For filling:
Line 9-inch-diameter cake pan with 1 1/2-inch-high sides with plastic wrap, leaving 5-inch overhang. Whisk egg yolks, 1/4 cup sugar, and Kahlúa in medium metal bowl to blend. Set bowl over saucepan of simmering water (do not allow bottom of bowl to touch water). Using electric mixer, beat until yolk mixture is thick and instant-read thermometer inserted into mixture registers 140°F for 3 minutes, about 9 minutes total. Remove bowl from over water. Continue to beat mixture until cool to touch, about 3 minutes. Beat whipping cream and espresso powder in another medium bowl until firm peaks form. Fold cream mixture into yolk mixture in 2 additions. Using clean dry beaters, beat egg whites in large bowl until soft peaks form. Gradually add remaining 1/4 cup sugar and beat until stiff and glossy. Gently fold whites into yolk mixture in 2 additions. Fold in chopped chocolate. Carefully place 1 cake layer in prepared pan (cake layer is very delicate). Spread filling evenly over cake (filling layer will be thick). Top with second cake layer; press gently to adhere. Fold plastic overhang over cake, then cover with foil. Freeze cake overnight. (Can be made 3 days ahead. Keep frozen.)

For glaze:
Bring first 3 ingredients to simmer in small saucepan. Remove from heat. Add chocolate; whisk until smooth. Transfer 1/2 cup glaze to small bowl; chill until cool and very slightly thickened but easily spreadable (if too thick, glaze will not spread smoothly on frozen cake), about 10 minutes.

Remove foil and plastic wrap from top of cake. Invert cake onto 9-inch-diameter cardboard round or tart pan bottom; place on rack set over rimmed baking sheet. Working quickly, spread thin layer of chilled glaze over top and sides of cake. Freeze until glaze is set, about 1 hour.

Rewarm remaining glaze over low heat until just warm and pourable. Transfer to 1-cup measuring cup. Pour half of glaze over top of cake. Working quickly and using offset spatula, spread glaze over top, allowing excess to run down sides of cake; spread quickly over sides (glaze will harden quickly on frozen cake). Pour remaining glaze over top of cake; spread quickly and smoothly over top and sides. Sprinkle coffee beans around top edge of cake. Freeze until firm and glaze is set, at least 4 hours. (Can be made 3 days ahead. Cover; keep frozen.)

To serve, dip long thin sharp knife into hot water, then wipe dry and cut cake into wedges, pulling knife out at bottom of cake to avoid tearing glaze and repeating for each slice.