Preheat the oven to 180°C. Grease and line a 9-inch square brownie tin with parchment paper; set aside.
In a small bowl, whisk together the flour and the baking powder; set aside.
Place the butter and the chocolate in a medium heatproof bowl set over a bot of boiling water - ensuring the water in the pot doesn't touch the bottom of the bowl. Stir together until melted and combined, then remove from the pot.
Using a hand whisk, incorporate the sugars into the chocolate mixture. Add the eggs, the yolk, and the vanilla; whisking until combined. Using a rubber spatula, fold the flour mixture into the batter until just combined - do not overwhip the batter.
Pour the batter into the prepared tin and bake in the preheated oven for 25-minutes, or until a skewer inserted into the centre of the brownie tin comes out clean. Leave to rest on a wire rack until completely cool.