A trifecta of chocolate stars in this uniquely constructed frozen dessert: decadent dark chocolate cake, rich white chocolate ganache, and luscious chocolate ice cream.
Cakes: Preheat oven to 350 degrees. Butter a 9-inch round cake pan (2 inches deep); line with parchment. Butter parchment, then dust with cocoa, tapping out excess. Repeat process with a 15 1/2-by-10 1/2-inch jelly-roll pan. In the bowl of a mixer fitted with the paddle attachment, beat together cocoa, flour, sugar, baking soda, baking powder, and salt on low speed until just combined. Add eggs, buttermilk, oil, and vanilla; beat to combine. Add water; increase speed to medium and beat until smooth, about 3 minutes.
Transfer 1 cup batter to prepared cake pan and remaining batter to prepared jelly-roll pan, spreading both batters evenly with an offset spatula. Bake until set and a tester inserted into centers comes out clean, 12 to 14 minutes. Transfer pans to wire racks and let cool 15 minutes. Invert cakes from pans; reinvert onto racks and let cool completely.
White Chocolate Ganache: Place chocolate in a medium bowl. Heat cream in a small saucepan over medium; pour over chocolate. Let stand 3 minutes. Gently stir with a spatula until fully incorporated. Cover and refrigerate until set but still spreadable, about 1 hour. If ganache is too firm, let stand at room temperature or beat with a mixer until softened.
Trim edges of rectangular cake. Top with ganache; spread evenly to edges. Using a ruler, cut cake evenly into quarters; stack on top of one another, gently pressing down to adhere layers. Cover and refrigerate 30 minutes. Using a ruler, cut cake lengthwise into 1-inch-wide strips, then cut each strip in half (they should be about 3 1/2 to 4 inches tall).
Transfer 9-inch cake to a 10-inch springform pan. Place cake strips around perimeter of cake, flush with edge of pan.
Spread ice cream over cake in pan; cover and freeze overnight. Just before serving, remove cake from freezer; unlatch pan, remove cake, and top with whipped cream and chocolate shavings.