Preheat the oven to 350°F. Prepare a 9-inch square metal baking pan by lining it with nonstick foil or spraying it with nonstick spray.

Place the butter in a microwave-safe bowl and heat in short bursts, stirring between bursts, until fully melted. Allow the butter to cool slightly but not solidify.

Stir the sugar into the melted butter until evenly combined.

Add the eggs one at a time, whisking well after each addition. Stir in the vanilla.

In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt until evenly distributed.

Add the dry ingredients to the wet mixture and stir until the batter is smooth and uniform, about 1 minute.

Pour and spread the batter evenly into the prepared pan, smoothing the top with a spatula or the back of a spoon.

Bake until a toothpick inserted into the center comes out with just a few moist crumbs attached, about 40 minutes. Start checking at 35 minutes if your oven runs hot.

Remove the pan from the oven and let the brownies cool completely in the pan on a wire rack before cutting.

Cut into 16 squares. Store at room temperature, covered well; the brownies also freeze well.