Preheat the oven to 325F and line an 9x5 loaf pan with parchement paper.
Brown the butter
In a medium saucepan, melt the better on medium heat. Once the butter melts fully and starts foaming, stir continuously to be able to see the color of the butter changing. You will smell a nutty aroma and notice the buter turning golden brown.
Once the butter is golden brown remove it from the heat and set aside.
Make the brown butter banana bread
In a bowl, mix the mashed bananas, granulated sugar, brown sugar, eggs, vanilla, milk, sour cream, and brown butter together until combined.
Add in the flour, baking soda, and salt and gently fold using a spatula. Stop mixing when the flour disappears and pour it in the prepared loaf pan.
Bake the brown butter banana loaf caeke in the preheated oven for 60-67 minutes. You will know your banana bread is ready when it is golden caramel colored on top and a wooden skewer inserted in the center or it comes out clean.
Allow the loaf cake to cool down in the pan for 10-15 minutes before transferring it to a cooling rack to cool down for a few more minutes before serving.
Make sure to use very ripe bananas to ensure that the banana flavor comes out as much as we want it to!