Preheat the oven to 350°F (175°C). Grease an 8×8 inch baking pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt until well combined.
In a large bowl, mix the melted unsalted butter and granulated sugar until smooth and combined.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the whole milk, beginning and ending with the dry ingredients. Mix until just combined and smooth.
Pour the batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 28 to 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Remove from the oven and allow the brownies to cool completely in the pan on a wire rack before cutting into 16 squares.