Preheat oven to 350 degrees F. Spray a loaf pan (I used a glass pan) with baking spray (I used coconut oil spray) or grease with butter.
Brown the butter: Melt the butter in a small saucepan over medium-low heat. Bring to a low boil, stirring constantly with a rubber spatula. Continue stirring until the butter turns golden and small brown flecks appear. Be careful to watch the butter closely as it can go from browned to burnt quickly. Immediately remove from the heat and continue stirring for 30 seconds longer. Set aside to cool slightly.
Place bananas in a large bowl and mash.
Add the brown sugar and brown butter to the bowl and whisk until well combined. Whisk in the egg and vanilla.
Add the cinnamon, nutmeg, baking soda and salt to the bowl and whisk until well combined.
Add the flour and stir with a rubber spatula until just combined.
Pour the batter into the prepared baking pan.
Bake for 50-60 minutes, until a tester inserted in the center comes out with just a few moist crumbs attached.
Let bread cool in the pan for 15 minutes and then remove to a wire rack to cool completely.