Preheat oven to 350°F. Grease or line a 9x13 baking dish.
In a large bowl, whisk together melted butter and sugar until smooth.
Add eggs and vanilla, then beat until combined.
Stir in mashed bananas until fully incorporated.
Fold in flour, baking powder, baking soda, and salt. Mix until just combined.
Gently stir in walnuts and chocolate chips, if using.
Spread batter evenly into the prepared pan.
Bake for 30–35 minutes, or until a toothpick inserted in the center comes out mostly clean.
Cool slightly before slicing into squares. Serve warm or at room temperature.