Preheat your oven to 350°F (175°C).
Grease your baking pan or line it with parchment paper.
In a medium saucepan, melt the butter over low heat and let it cool slightly.
In a large mixing bowl, whisk together the melted butter and sugar. Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt.
Gradually add the dry mixture to the wet ingredients, folding gently with a spatula until just combined.
Pour the brownie batter into the prepared baking pan, spreading it evenly with a spatula.
Bake in the preheated oven for 25-30 minutes. Check for doneness with a toothpick.
Once baked, let the brownies cool in the pan for about 10 minutes before lifting them out to cool completely on a wire rack.