1. Preheat the oven to 350°F and grease or line a 9×13-inch baking pan.

2. In a large bowl, whisk together the melted butter and granulated sugar until combined.

3. Add the eggs, mashed bananas, sour cream, and vanilla extract, then mix until smooth.

4. Stir in the flour, baking soda, salt, and cinnamon just until no dry streaks remain.

5. Spread the batter evenly in the prepared pan.

6. Bake for 23 to 28 minutes, or until the center is set and a toothpick comes out with a few moist crumbs.

7. Let the bars cool slightly while you prepare the frosting.

8. In a saucepan over medium heat, melt the butter for the frosting and continue cooking until it turns golden brown and smells nutty.

9. Remove from the heat and whisk in the powdered sugar, vanilla extract, and milk until smooth and spreadable.

10. Spread the warm brown butter frosting over the slightly warm bars.

11. Sprinkle chopped walnuts or pecans on top.

12. Let the frosting set completely before slicing and serving.