Preheat your oven to 350°F (175°C). Grease a 9×9 inch (23×23 cm) square baking pan or line it with parchment paper.
In a medium bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Set aside.
In a large bowl, whisk the melted unsalted butter and granulated sugar until smooth and combined.
Add the eggs one at a time to the butter and sugar mixture, whisking well after each addition.
Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the whole milk. Begin and end with the dry ingredients. Mix until just combined; do not overmix.
Pour the batter into the prepared baking pan and spread it 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 but no wet batter.
Remove from the oven and let cool in the pan on a wire rack for at least 20 minutes before cutting into 16 squares.
Serve and enjoy your moist, chocolatey cake brownies!