Prepare the Brown Butter:
Brown the butter over medium to low heat for about 10 minutes until you see brown flakes.
Immediately remove from the heat and transfer into a baking bowl.
Wait 5 to 10 minutes before mixing with the brown sugar.
Mix the Wet Ingredients:
Once the brown butter has cooled slightly, add the brown sugar and mix until fully combined.
Add the mashed bananas, egg, vanilla extract, and milk. Mix until fully incorporated.
Combine the Dry Ingredients:
In a separate bowl, whisk together the flour, baking powder, and salt.
Slowly and gently fold the dry ingredients into the wet batter until just combined.
Prepare the Cinnamon Sugar Mixture:
Melt 5 tablespoons of unsalted butter.
Add the brown sugar and cinnamon to the melted butter and mix until fully combined. Set aside.
Assemble the Banana Bread:
Preheat your oven to 350°F (175°C).
Line a 9×5 inch baking dish with parchment paper or grease it well.
Pour half of the banana bread batter into the prepared baking dish.
Swirl in half of the cinnamon sugar mixture.
Pour the remaining banana bread batter on top, then swirl the remaining cinnamon sugar mixture over the top.
Bake the Bread:
Bake at 350°F for 55 to 65 minutes.
Check on the bread halfway through baking. If it is getting too brown, cover the top with aluminum foil, tenting it to allow the bread to rise and breathe.
Test for doneness at 55 minutes by inserting a knife into the center. If it comes out clean, the bread is done. If not, continue baking and check again.
Cool the Bread:
Let the bread cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely for 1 hour.
Prepare the Cream Cheese Frosting:
While the bread is cooling, make the cream cheese frosting.
In a bowl, beat together the room temperature cream cheese, powdered sugar, milk, and vanilla extract until smooth and creamy.
Frost and Serve:
Once the bread is completely cool, spread an even layer of cream cheese frosting on top.
Slice into 12 equal pieces and enjoy!