Preheat the oven to 350°F. Spray a 9x5-inch (or 8.5x4.5-inch) loaf pan with baking spray (such as coconut oil spray) or grease with butter.

Brown the butter: Melt the butter in a small saucepan over medium-low heat. Bring it to a low boil, stirring constantly with a rubber spatula. Continue stirring until the butter turns golden and small brown flecks appear. Watch closely, as browned butter can quickly burn. Immediately remove from heat and continue stirring for 30 seconds. Set aside to cool slightly.

In a large mixing bowl, combine the mashed banana, brown sugar, and browned butter. Whisk until well combined. Whisk in the egg and vanilla extract.

Add the cinnamon, baking soda, and salt, whisking until fully incorporated.

Stir in the flour using a rubber spatula until just combined. Be careful not to overmix. Pour the batter into the prepared loaf pan.

Bake for 45-55 minutes, or until a tester inserted in the center comes out clean. Avoid overbaking. Let the bread cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.