Melt the butter and chocolate in a medium, heavy saucepan set over very low heat. Stir constantly until almost fully melted. Remove the pan from the heat and stir until the chocolate is completely melted and smooth.

Whisk together the flour, baking powder, and salt in a medium bowl.

Using an electric mixer, beat the eggs in a large bowl until frothy, about 45 seconds. Add the granulated and brown sugar and beat until thick and smooth, about 1 minute. Beat in the melted chocolate mixture and the vanilla. With the beaters on low speed, mix in the flour mixture just until completely blended. Cover the bowl with plastic wrap and refrigerate until the dough is firm, at least 4 hours but preferably overnight.

Preheat the oven to 350°F. Line 1 or 2 cookie sheets with parchment paper.

Place the confectioners' sugar in a medium bowl. Set a sheet of wax paper on the work surface in front of you. Using a small spoon, scoop chunks of dough and roll them between your hands into 1-inch balls. Place the balls on the wax paper, forming enough for 1 cookie sheet. (There's no getting around messy, sticky hands; just wash them after each batch.) Drop about 5 balls at a time into the confectioners' sugar and shake the bowl to fully and generously coat them. Arrange them about 2 inches apart on the prepared sheet(s).

Bake for 11 to 12 minutes or until the cookies are puffed and crackled on top. The tops should be soft, even a little wet looking, but the edges should feel mostly firm. (If using 2 cookie sheets, rotate them from top to bottom and front to back about halfway through baking.) Slide the parchment off the sheet and onto a wire rack. After a few minutes, remove the cookies from the paper using a thin metal spatula and place them directly onto racks to cool.

STORE, layered between sheets of wax paper, in an airtight container for up to 4 days; or freeze for up to 2 months.