Preheat oven to 400 degrees. Line baking sheets with Silpats; set aside. In a small bowl, sift together flour, baking powder, and salt; set aside.

In a heat-proof bowl set over a pot of simmering water, or the top of a double boiler melt together unsweetened and semisweet chocolates and butter; set aside.

In the bowl of an electric mixer fitted with the whisk attachment, whip eggs, sugar, and vanilla extract on medium speed until light and fluffy, about 3 minutes. Add melted chocolate mixture, and combine on low speed. Add dry ingredients, and continue to beat on low speed until almost combined, about 1 minute. Remove bowl from mixer; stir in milk chocolate by hand.

Using 1½-ounce ice-cream scoop, drop dough onto prepared baking sheets about 3 inches apart. Bake until set, 12 to 15 minutes. Let cookies cool completely on baking sheets. Remove and serve, or store in an airtight container for up to 3 days.