Preheat the oven to 350 F. Line a 9-inch cake pan with parchment and spray well with nonstick cooking spray. Whisk together the flour, cocoa powder, salt, and baking powder in a small bowl. Set aside for now.
Cube the butter and place it in a medium saucepan over medium-low heat. Stir occasionally as the butter melts. Add the sugar, and stir until it melts. Don’t allow the mixture to come to a boil.
Remove the pan from the heat, and let it cool to lukewarm. Once it has cooled, add the eggs, one at a time, whisking well between each addition. The mixture will start out grainy, but as you add the eggs, it will become shiny and smooth. Whisk the vanilla in. Finally, add the dry ingredients, and stir them in with a spatula.
Scrape the brownie batter into the prepared pan, and bake it for 22-24 minutes, until a toothpick comes out with just a few moist crumbs attached. Cool the brownie layer completely before proceeding.