1. Preheat oven to 325°. In a heatproof bowl set over a pan of barely simmering water (but not touching it), stir bittersweet chocolate and butter until smooth, 5 minutes. Remove bowl from over water; whisk in sugar, eggs, and vanilla.
2. In another bowl, mix flour, baking powder, baking soda, and salt. Add to chocolate mixture and stir until well blended. Stir in white chocolate. Cover and chill dough until firm, at least 1 hour.
3. Shape dough into 2-inch balls and place about 3 inches apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets.
4. Bake until set at the edges but still soft in the center, 12 to 15 minutes; if baking more than one pan at a time, switch pan positions halfway through baking.
5. Let cool for 5 minutes on sheets; transfer to racks to cool completely.