In a saucepan over low heat (or microwave in short bursts), melt the butter and chocolate together until smooth. Let cool for 5 minutes.
In a mixing bowl, beat eggs, granulated sugar, and brown sugar on high speed for about 3-4 minutes, until pale and slightly thickened. This step gives you that crackly top.
Slowly pour the cooled chocolate-butter mixture into the eggs while mixing on low. Add vanilla extract.
In a separate bowl, whisk together flour, cocoa powder, baking powder, and salt. Add to wet ingredients and mix until just combined. Chill dough for 30-60 minutes (optional, but helps with shape and texture).
Preheat oven to 350°F. Scoop 1.5-2 tbsp of dough onto a parchment-lined baking sheet, spacing about 2 inches apart. Bake for 10-12 minutes, until edges are set but centers are soft. They will firm up as they cool.
Let cookies cool on the pan for 5 minutes, then transfer to a wire rack. Dust with powdered sugar, and enjoy!