Beat or whisk the butter, granulated sugar, and brown sugar together in a large bowl. Add the eggs and beat again.
Stir in flour and salt, just until combined.
In a separate medium bowl, mash the bananas and sprinkle the baking powder on top. Stir to combine. Pour half of the batter into the bowl with the bananas and stir to combine. Set aside.
Add the cocoa powder and most of chocolate chips, reserving a handful for sprinkling on top of the brownies, into the remaining half of the batter. Stir to combine.
Dollop spoonfuls of about half of the brownie batter into the prepared pan. It doesn't need to cover the bottom of the pan. Pour the banana bread mixture over the brownie mixture. Drop spoonfuls of the remaining brownie batter on top, then use a knife to gently swirl the mixtures together a bit. Sprinkle with the extra chocolate chips.
Bake for 40 to 45 minutes until a toothpick inserted into the center of the brownies comes out clean with just a few crumbs on it. Cool completely before slicing into squares.