Put chocolates and butter in a medium metal bowl and set bowl over a pan filled with 1 in. of simmering water. Cook, stirring occasionally, until melted, then remove from heat and let cool slightly. Whisk in eggs and sugar, mixing until combined. Then whisk in flour, baking powder, and salt. Chill dough, covered, until firm, about 2 hours.
Let dough sit at room temperature 15 minutes. Meanwhile, preheat oven to 350° and line 2 baking sheets with parchment paper. Scoop 1 tbsp. portions of dough, rolling each into a ball, and put onto sheets 1 in. apart. Bake cookies until they no longer look wet on top, about 8 minutes. Let cool on baking sheets.
Make ahead: Batter up to 1 day; baked cookies up to 2 days, airtight.