Preheat oven to 350 degrees. Coat two 12-by-17-inch rimmed baking sheets with cooking spray. Line each with parchment paper; generously coat parchment with more cooking spray. Sift flour, baking powder, and salt together in a small bowl; set aside.
Beat egg yolks and 1/4 cup plus 2 tablespoons granulated 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 remaining 1/4 cup plus 2 tablespoons granulated sugar, and beat until stiff (but not dry) peaks form. Fold egg-white mixture into yolk mixture in three additions, folding in the flour mixture with the last addition of whites.
Working quickly, divide batter among lined sheets; smooth tops with an offset spatula. Bake, rotating sheets halfway through, until cakes are pale golden and springy to the touch, 12 to 15 minutes.
Meanwhile, lay two clean kitchen towels on work surface; sift confectioners' sugar over towels to lightly coat. Immediately run a knife around edges of cakes; invert onto sugar-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 to a wire rack to cool completely, about 1 hour.
Put pistachio paste in a large bowl, and stir with a rubber spatula until smooth. Beat 1 cup cream in the bowl of a mixer fitted with the whisk until soft peaks form, and fold into pistachio paste. Unroll cooled cakes (do not remove from towels), and spread pistachio mousse evenly 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, and wrap cakes well in plastic wrap. Freeze until mousse is firm, at least 1 hour or up to 1 month.
Beat remaining 3/4 cup cream in the bowl of a mixer fitted with the whisk until soft peaks form. Spread whipped cream over cakes; gently press white-chocolate bark into whipped cream. To serve, trim both ends of each roulade with a serrated knife; cut each cake into 6 pieces (alternate diagonal and straight cuts to give each piece a flat base and angled top).
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