Preheat oven to 400 degrees. Coat a 15-by-10-inch rimmed baking sheet with cooking spray, and line with parchment. Using a mixer with the whisk attachment, beat eggs, confectioners' sugar, flours, cocoa powder, and salt on medium-high speed for 5 minutes. Reduce speed to low, and add butter. Raise speed to medium-high, and beat for 1 minute.
Whisk egg whites in a clean mixer bowl until foamy. Gradually add granulated sugar, and beat until stiff (but not dry) peaks form. By hand, whisk a third of egg-white mixture into the cocoa mixture, then gently fold in remaining egg-white mixture in 2 batches. Pour batter into prepared baking sheet, and smooth top.
Bake, rotating halfway through, until bottom is set and top springs back when touched, about 8 minutes. Let cool for 5 minutes. Run tip of a knife around edges of cake. Sprinkle top generously with granulated sugar to prevent sticking, then invert cake onto a wire rack set over a piece of parchment. Peel off parchment. Reinvert cake, and let cool for 10 minutes. Cut out 16 rounds with a 2 3/8-inch cutter. Use immediately or store. To store, lay rounds on a parchment-lined baking sheet, wrap in plastic, and refrigerate for up to 3 days.
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