Preheat oven to 350 degrees. Coat two 12-by-17-inch rimmed baking sheets with cooking spray. Line each with parchment paper; generously coat with more spray. Sift flour, baking powder, cocoa, and 1/2 teaspoon salt together into a small bowl; set aside.
Beat yolks and 3/4 cup sugar in the bowl of a mixer fitted with the whisk until pale yellow and thick. Beat in vanilla; set aside.
Beat egg whites in the clean bowl of a mixer fitted with the whisk until soft peaks form. Slowly add 3/4 cup sugar; beat until stiff (but not dry) peaks form. Fold egg-white mixture into yolk mixture in 3 additions, folding in flour mixture with the last addition of whites. Divide batter among sheets; smooth tops with an offset spatula. Bake, rotating sheets halfway through, until cakes are springy to the touch, 15 to 20 minutes.
Meanwhile, lay 2 clean kitchen towels on work surface; sift cocoa over towels to lightly coat. Immediately run a knife around edges of cakes; invert onto cocoa-dusted towels, and carefully remove parchment. Starting with a long side, gently roll each cake in a towel (as if towel were the filling). Transfer cakes to a wire rack to cool completely, about 1 hour.
Put chestnut puree, remaining 3/4 cup sugar, and pinch of salt in the bowl of a mixer fitted with the paddle; mix on medium speed until smooth, about 3 minutes. In a separate bowl, whip cream until soft peaks form; fold into chestnut mixture. Unroll cooled cakes; spread 1 cup chestnut mousse in an even layer on top of each. Carefully re-roll cakes, using towels to help bring cake up at each turn (do not roll towels into filling). Remove towels; wrap cakes well in plastic wrap. Freeze until mousse is firm, at least 1 hour or up to 1 month. (Remaining mousse can be frozen in an airtight container up to 1 month; thaw, and beat with the paddle attachment until smooth before using.)
Spread remaining mousse over cakes; gently press chocolate bark into mousse to coat evenly.To serve, trim ends with a serrated knife, and cut each log into 6 pieces (alternate diagonal and straight cuts to give each piece a flat base and angled top).
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