Preheat your oven to 325°F (fan-assisted) or 340°F (conventional). Line a baking sheet with parchment paper.
Place the chopped dark chocolate and butter in a heatproof bowl set over gently simmering water. Stir until melted and smooth, then mix in the vanilla extract. Remove from heat and let cool slightly.
In a separate bowl, whisk the eggs, granulated sugar, and brown sugar using an electric mixer on high speed for about 5 minutes, until pale, thick, and fluffy.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Stir in the chocolate chips.
Gently fold the melted chocolate mixture into the whipped egg mixture, keeping as much air in the batter as possible.
Carefully fold in the dry ingredients until just combined. Do not overmix.
Scoop tablespoon-sized portions of batter onto the prepared baking sheet, leaving space between each.
Bake for 12–14 minutes, until the tops look crackly and just set.
Remove from the oven and allow the brookies to cool on the tray for 10 minutes before transferring to a wire rack to cool completely.