Preheat the oven to 350°F (175°C). Grease an 8×8-inch baking pan or line it with parchment paper.
In a large bowl, combine the mashed bananas, melted butter, and granulated sugar. Mix well until smooth.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, cocoa powder, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Fold in the semi-sweet chocolate chips evenly into the batter.
Pour the batter into the prepared baking pan and spread it evenly.
Bake 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 15 minutes before slicing into 12 squares.
Serve warm or at room temperature.