Heat oven to 350°F. Line 8 x 2-inch round cake pan with foil. Grease second 8 x 2-inch pan; line bottom with waxed paper; grease paper.
Beat cheese, sugar, egg, flour, vanilla in bowl until smooth. Fold in chips. Transfer to foil-lined pan.
Mix flour, cocoa, baking soda and powder, and salt in bowl. Beat butter, sugar and vanilla in large bowl until combined, 2 minutes. Beat in melted chocolate, then egg. On low speed, beat in half the flour mixture, buttermilk, then remaining flour mixture. Scrape into paper-lined pan, spreading evenly; tap pan lightly on counter to remove air bubbles.
Bake cakes in 350°F oven 30 minutes, until cheesecake is set and toothpick inserted in center of chocolate cake tests clean. Let cakes cool in pans on rack 20 minutes. Refrigerate cheesecake in pan, wrapped. Unmold chocolate cake on rack; remove paper; let cool. (Cakes can be made 2 days ahead; refrigerate cheesecake, wrapped; store other cake, wrapped, at room temperature.)
Cut piece of waxed paper 26 x 4-1/2 inches. Place on top of a sheet of foil. Microwave chocolate in 2-cup glass measure on high until melted, 1 minute; stir. Microwave 30 seconds. Stir until smooth. Stir in syrup; mixture will thicken slightly. Using offset spatula, spread chocolate-corn syrup mixture over waxed paper, spreading to edges. Cover with plastic wrap; let stand until firm, 2 hours. (Can be made day ahead and stored, tightly wrapped, at room temperature.)
Using 1/3 cup mousse, spread thin layer around cake side. Remove waxed paper from chocolate; wrap chocolate, pointed side up, around cake, trimming to fit. Mound remaining mousse on top. Chill 1 hour, until mousse is set. (If not using wrapper, chill mousse 15 minutes; spread over sides and top of cake.)
Once cakes are cool, prepare Chocolate Mousse.
Lift Chocolate Wrapper with plastic wrap and gently stand up around outside edge of 8-inch cake pan to make wrapper more pliable (it should remain firm). Return to flat surface. Carefully peel away plastic wrap from top. Trim any ragged edges from chocolate. Using large round cookie cutter (at least 3-3/4 inches), cut crown top along one long edge of strip (save scraps for snacking). Slice chocolate cake in half horizontally. Place bottom layer on cake pedestal. Spread 3 tablespoons mousse over top of cake. Remove cheesecake layer from pan; remove foil. Place on top of chocolate cake layer. Spread with 3 tablespoons mousse. Top with chocolate layer.
Place coffee in small microwave-safe bowl. Sprinkle gelatin over top; let stand 5 minutes to soften. Microwave on high 10 seconds, stirring to dissolve gelatin.
Bring medium-size saucepan half full of water to bare simmer. In medium-size metal bowl that fits over water in saucepan without touching water (or in top of double boiler), combine eggs and 4 tablespoons sugar. Whisk in gelatin mixture. Place bowl over warm water; beat with mixer until instant-read thermometer inserted in mixture registers 140°F, 7 minutes. Continue beating over warm water for 3 minutes. Remove pan from heat. Fold in unsweetened pre-melted chocolate.
In large bowl, beat remaining 2 tablespoons sugar and heavy cream until medium-soft peaks form. Fold some of whipped cream into chocolate mixture to lighten. Fold chocolate mixture into remaining whipped cream.