Preheat your oven to 350°F (175°C) and grease a baking pan.
In a mixing bowl, combine melted butter and granulated sugar. Mix in eggs, mashed bananas, and vanilla extract until well combined.
In another bowl, whisk together flour, baking soda, and salt. Gradually add to the banana mixture, stirring until just combined. If using, fold in chopped walnuts or pecans.
Pour the batter into the prepared baking pan and bake for 25 to 30 minutes, or until a toothpick inserted comes out clean.
For the glaze, melt the butter in a saucepan over low heat. Remove from heat and stir in powdered sugar, milk, and vanilla extract until smooth.
Once the brownies are cooled, pour the glaze over the top and let it set before slicing.
Notes
These brownies can be stored in an airtight container for up to a week.