Preheat oven to 350°F (175°C) and grease an 8×8-inch baking pan with parchment paper.
Whisk together the melted butter and sugar until smooth and creamy.
Add eggs and vanilla extract, whisking until fully combined.
In a separate bowl, mix together flour, baking powder, salt, and banana pudding mix.
Gradually fold dry ingredients into the wet mixture, stirring until just combined.
Stir in the mashed bananas until fully incorporated into the batter.
Pour the batter into the prepared pan, spreading it out evenly.
If using mini chocolate chips, sprinkle them over the top of the batter.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the brownies cool completely in the pan before cutting them into squares and serving.