Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking pan or line it with parchment paper for easy removal.
In a medium saucepan, melt the unsalted butter over low heat. Remove from heat and let it cool slightly.
In a large mixing bowl, combine the melted butter and granulated sugar. Mix well, then add the eggs one at a time, stirring to incorporate after each addition. Add the vanilla extract and mix until smooth.
In another bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.
Fold in the semi-sweet chocolate chips and/or chopped nuts if desired.
Pour the brownie batter into the prepared baking pan, spreading it out evenly.
Place the pan in the preheated oven and bake for 25-30 minutes. The brownies are done when a toothpick inserted in the center comes out with a few moist crumbs.
Remove from the oven and let the brownies cool in the pan for 15-20 minutes before transferring them to a wire rack to cool completely.
Once cooled, cut into squares and serve as desired.