Preheat oven to 350°. Butter a 9″x 13″pan and line with parchment paper.
Whisk together flour, baking powder, and salt. Set aside.
Melt chocolate and butter together in the top of a barely simmering double boiler. Remove from heat.
Using the whisk attachment of an electric mixer, beat 3 eggs and 1 cup sugar on high speed for about 5 minutes, or until thick and fluffy. Reduce speed to low and add chocolate mixture and 1 teaspoon vanilla. Mix well. Add flour mixture, stirring until just combined. Spread into prepared pan and set aside.
Using an electric mixer, beat mascarpone cheese, 2 eggs, egg yolks, 1/3 cup sugar, and 1/2 teaspoon vanilla. Mix until smooth. Pour over chocolate mixture.
Bake about 35 minutes, or until cheese mixture is golden and set. Cool completely on a wire rack.