Preheat the oven to 350°F. Grease and line the bottoms of three 6-inch cake pans with parchment paper and set aside.
Place the butter and chocolate in a heat-safe bowl set over a saucepan of simmering water. Cook until the butter and chocolate melt. Stir together and set aside to cool.
In a medium bowl, whisk together the cocoa powder, flour, baking powder, and salt. Set aside.
In a large bowl, whisk together the eggs and sugar until pale and frothy, 3 to 5 minutes. Add the vanilla extract and mix to combine. Pour in the cooled chocolate mister and whisk until combined. Add the cocoa mixture. Use a rubber spatula to stir the batter together until there are no visible streaks of dry flour. A few lumps are okay.
Divid the batter evenly between the prepared pans. Bake for 30 to 40 minutes, or until a wooden skewer inserted into the center comes out with a few moist crumbs. Do not overbake.
Allow the brownie cakes to cool on a wire rack for 30 minutes. Once the pans are cool enough to handle, run a thin knife around the inner edge of the pan and unmold the cake layers. Allow the cake layers to completely cool.