Preheat the oven to 350°F (175°C). Grease the baking pan or line it with parchment paper for easy removal.
In a medium microwave-safe bowl, melt the unsalted butter. This should take about 30-40 seconds in the microwave.
Once melted, remove the bowl from the microwave and mix in the granulated sugar until well combined.
Add the eggs, one at a time, mixing well after each addition. Then, stir in the vanilla extract.
In a separate bowl, whisk together the cocoa powder, flour, salt, and baking powder.
Gradually incorporate the dry ingredients into the wet mixture using a rubber spatula or wooden spoon. Mix until just combined; do not overmix.
If desired, fold in chocolate chips or nuts for added texture and flavor.
Pour the brownie batter into the prepared baking pan, spreading it evenly.
Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs (but no wet batter).
Let the brownies cool in the pan on a wire rack for about 10 minutes before slicing them into squares.