Watch the butter closely once it starts foaming — it goes from browned to burnt in under a minute. Pull it the moment you smell nuts and see brown flecks on the bottom of the pan.
Instructions
Melt the butter in a light-colored saucepan over medium heat, swirling often, until it turns amber and smells nutty, 4-5 minutes. Pour into a large bowl to cool slightly.
Preheat the oven to 350°F and grease a 9x5 loaf pan.
Whisk the mashed bananas, brown sugar, egg, and vanilla into the browned butter.
Add the flour, baking soda, salt, and cinnamon. Fold just until no dry streaks remain — do not overmix.
Pour into the pan and bake 50-55 minutes, until a toothpick comes out with a few moist crumbs.
Cool in the pan 10 minutes, then turn out onto a rack to cool completely before slicing.