Prepare the Brown Butter: In a saucepan over low to medium heat, melt the butter. Continue stirring as it melts, watching for golden brown flecks to form at the bottom. This takes about 5-10 minutes. Once browned, let it cool for 10 minutes, then mix in the brown sugar.
Make the Banana Bread Batter: Add the mashed bananas to the brown butter mixture, stirring to combine. Next, mix in the egg, milk, and vanilla extract until fully incorporated.
Mix Dry Ingredients: In a separate bowl, whisk together the flour, cinnamon, baking powder, and salt. Gently fold these dry ingredients into the banana mixture, ensuring no lumps.
Prepare the Cheesecake Filling: In another bowl, beat the softened cream cheese until fluffy. Add the sugar, egg, vanilla extract, and flour, mixing until smooth and creamy.
Assemble the Layers of the Cheesecake Banana Bread: Pour half of the banana bread batter into a greased 9×5-inch (23×13 cm) loaf pan. Spread the cheesecake filling evenly over the batter, then top with the remaining banana bread batter.
Bake the Cheesecake Banana Bread: Preheat your oven to 350°F (175°C) and bake for 65-75 minutes. If the top browns too quickly, cover with foil. Check for doneness by inserting a toothpick; it should come out with just a few crumbs.
