In a heatproof bowl, combine the butter and chopped chocolate, and set over a saucepan filled with a few inches of simmering water over low heat. Let melt, 3 to 4 minutes, then stir until smooth. Remove the bowl from the pan and let cool slightly.

In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt to combine and get rid of any lumps.

In a large bowl, combine the brown sugar, eggs, vanilla, and ½ cup granulated sugar, and beat with a mixer on medium-high speed until light and smooth, 2 to 3 minutes. Add the melted chocolate mixture and beat until combined. With the mixer on low speed, add the flour mixture and beat until just combined, 30 seconds to 1 minute. Cover the dough and refrigerate until firm, at least 2 hours and up to 4 hours.

Preheat the oven to 350°F. Line 2 baking sheets with parchment paper. Place the remaining 1 cup granulated sugar in a shallow bowl and the powdered sugar in a second shallow bowl. Scoop the dough into balls (about 1 tablespoon each). Roll first in the granulated sugar, then in the powdered sugar to coat completely. Place on the baking sheet, about 2 inches apart. Bake until the tops of the cookies are cracked and the edges are firm, 10 to 12 minutes. Let cool 5 minutes on the baking sheets, then remove to racks to cool completely.