Heat oven to 350 degrees. Butter a 9-by-13-inch baking pan, and line with parchment. Whisk together flour, baking powder, and salt, and set aside. In the top of a barely simmering double boiler, melt together chocolate and butter. Remove from heat.
In the bowl of an electric mixer fitted with the whisk attachment, beat together 3 eggs and 1 cup sugar on high speed until thick and fluffy, about 5 minutes. On low speed, add reserved chocolate mixture and 1 teaspoon vanilla extract. When combined, add flour mixture. Stir until just combined. Spread mixture evenly into prepared pan. Set aside.
In the clean bowl of the electric mixer fitted with the paddle attachment, beat together mascarpone cheese, remaining eggs and yolks, remaining sugar, and remaining vanilla on medium speed, until smooth. Pour over chocolate mixture. Bake until cheese mixture is golden and set, about 35 minutes. Transfer to a wire rack to cool completely. Cut into about sixty 1-by-1 1/2-inch pieces.