Start by browning your butter. In a medium saucepan, melt 1/2 cup of unsalted butter over medium heat, stirring constantly. The butter will start to foam, and then it will turn a golden brown and smell nutty. Be careful not to burn it! Once it’s beautifully browned, remove the pan from heat and let the butter cool for about 10 minutes.
In a large mixing bowl, combine your cooled brown butter and 1 cup of brown sugar. Mix until smooth. Add in the mashed bananas and stir until everything is well combined.
Next, add your egg, vanilla extract, and 1/3 cup of milk. Mix until incorporated.
In a separate bowl, whisk together 2 cups of all-purpose flour, 1 1/2 teaspoons of baking powder, and 1/4 teaspoon of salt. Gently fold in 1 1/4 cups of crushed Oreos into the dry ingredients. Make sure to leave some chunks of Oreos for that extra texture—both small and big pieces work great!
Gradually add the dry ingredients into the wet mixture. Stir until just combined, being careful not to overmix. Once the batter is ready, fold in 3/4 of the Oreo mixture.
Line a 9×5 inch loaf pan with parchment paper or grease it well. Pour the batter into the prepared pan, spreading it out evenly. Sprinkle the remaining crushed Oreos on top.
Bake at 350°F (175°C) for 55-65 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs. Every oven is different, so start checking around the 55-minute mark.
Once the brown butter oreo banana bread is done, let it cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
While your bread is cooling, whip up the cream cheese icing. In a small bowl, combine 2-3 tablespoons of room-temperature cream cheese with 1 tablespoon of milk. Add in 1 cup of powdered sugar, and whisk until smooth and drizzle-able.
Once the brown butter oreo banana bread has cooled, drizzle the cream cheese icing generously over the top. Slice and enjoy!