Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking pan or line it with parchment paper.
Place the ripe bananas in a large mixing bowl and mash until mostly smooth.
Add the melted butter, granulated sugar, eggs, sour cream, and vanilla. Whisk until evenly combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Add the dry ingredients to the banana mixture. Gently fold until just combined, being careful not to overmix.
Fold in chopped walnuts or mini chocolate chips if desired. For a peanut butter variation, gently swirl a few spoonfuls through the batter.
Spread the Banana Bread Brownies recipe batter evenly in the prepared baking pan.
Bake for 25–30 minutes, or until the center is set and a toothpick inserted into the middle comes out clean or with a few moist crumbs.
Allow the brownies to cool completely in the pan. Add brown butter icing if desired.
Slice into squares or bars and serve.