First, preheat the oven to 350 degrees.
Second, take 1 stick of salted butter, place into a pot, and put on the stove over medium-high heat.
Third, whisk the butter until it starts to foam on top and begins to turn brown. When it starts to brown, remove from the heat.
Pour the brown melted butter into a separate bowl and put in the fridge to chill for 10 minutes.
Next, peel your brown bananas and place them into a large bowl.
Then, take a fork and mash your bananas until there are no more large chunks or pieces of banana.
Add the 3 eggs, vanilla extract, white and brown sugar, and salt to the mashed bananas and mix well.
Spread a little bit of butter (or cooking spray) on the inside of the loaf pan so that the parchment paper sticks to the sides and holds well.
Then, cover the inside of your loaf pan with two sheets of parchment paper. (I also used my scissors to cut off the parchment paper overhang)
Now, add the cooled brown butter to the mashed banana mixture. I like to add it slowly because the butter might still be warm. You don't want to have scrambled eggs, so I like to temper it. That just means that I pour the brown butter in slowly and whisk constantly to bring the temperature down and not expose the eggs to high heat immediately.
Next, add the 2 cups self-rising flour to the mashed banana mixture and mix just until it comes together. (You don't want to overmix it.)
Then, pour your brown butter banana bread batter into the prepared loaf pan, place in the preheated oven, and bake for 50-55 minutes or until golden brown.
After the banana bread comes out of the oven, place it onto a wire rack to cool before slicing.
Finally, slice the banana bread and serve with softened butter!