Brown the butter: Melt over medium heat, swirling until golden and nutty-smelling. Cool slightly.
Preheat oven to 350°F (175°C). Grease or line a loaf pan.
In a bowl, combine brown butter and brown sugar. Add eggs, mashed bananas, vanilla. Stir until smooth.
In another bowl, whisk flour, baking soda, salt, cinnamon.
Mix dry into wet until just combined. Fold in nuts.
Pour into pan. Bake for 50–60 min. Toothpick should come out clean (or with just a few moist crumbs).
