For this log, chocolate cake is rolled with pistachio ice cream, clad in chocolate, and frozen.
Preheat oven to 350 degrees. Coat a 12-by-17-inch rimmed baking sheet with cooking spray. Line with parchment paper; spray paper. Into a small bowl, sift flour, cocoa, baking powder, and salt; set aside.
In the bowl of an electric mixer, whisk yolks and half the sugar until thick and pale. Beat in vanilla. In a clean bowl, beat egg whites, with clean whisk, until soft peaks form. Slowly add remaining sugar; beat until stiff (but not dry) peaks form. Fold egg whites into yolk mixture in three batches; add flour mixture with last batch.
Spread batter evenly on prepared baking sheet. Bake until cake springs back to touch, 15 to 20 minutes. Run a small, sharp knive around edges to loosen, and invert cake onto clean kitchen towel dusted with cocoa powder. Peel off parchment paper. starting at a short side, roll into a log, incorporating towel. Transfer to a wire rack; let cool, about 1 hour.
Unroll cake; spread ice cream evenly over top, leaving 1/2-inch border on all sides. Reroll (without towel). Arrange, seam side down, on parchment-lined baking sheet; freeze until ice cream is firm, at least 1 hour. Run a serrated knife under hot water and pat dry. Trim ends of log as desired.
Wrap log in chocolate wood-grain: Tuck one end of chocolate-coated acetate under cake while lifting other end up and over cake (chocolate side should be facing cake), being careful not to let chocolate touch the cake until the sheet is ready to be tucked under at other side. Place, seam side down, on an inverted baking sheet, and return to freezer. Let stand until the chocolate has hardened, about 10 minutes.
When ready to serve, remove cake from freezer. Carefully peel acetate from cake; gently break off ends of chocolate wrapping to line up with ends of cake. Garnish with chocolate leaves, if desired.
Time the preparation of the Chocolate Wood-Grain so that it is ready when you remove the ice-cream-filled cake from freezer in step four.