Preheat and prep your pan: Arrange a rack in the bottom third of the oven and preheat to 350 degrees. Line your 8×5-inch loaf pan with parchment paper. Spray the inside with cooking spray or grease with butter.
Make the browned butter: In a heavy-bottomed skillet, melt the butter over medium-low heat. Continue to cook; the butter will foam and then begin to turn golden, then nut brown; whisk occasionally. Keep a close eye to avoid burning. When the butter is nut brown, remove from heat. Pour into a large mixing bowl and cool to room temp.
Mash bananas: While butter cools, peel the bananas and add them to a small bowl. Using a potato masher or a fork, mash until only a few small chunks remain.
Combine remaining ingredients: Once your butter has cooled, add maple syrup to butter and whisk to combine. Beat in eggs one at a time then add vanilla and the mashed bananas. Stir using a rubber spatula.
Add baking soda, baking powder, kosher salt, cinnamon, and allspice. Stir until well combined. Add flour and milk. Gently stir with a rubber spatula until the ingredients are just combined.
Bake the bread: Pour the batter into your prepared loaf pan. Bake for 50-65 minutes or until a toothpick inserted comes out clean. The baking time will vary depending on the ripeness of your bananas. I like to start checking around 50 minutes and then every 4-5 minutes until it looks done.
Let cool in the loaf pan for 10 minutes before transferring to a wire rack. Then cool for 10 more minutes before slicing. Enjoy!