In a small saucepan over low heat, add the unsalted butter. Let it melt, then add the dry milk powder. Whisk continuously until the butter becomes an amber-brown color and has a nutty, sweet smell. Foam and brown bits are normal. Keep a very close eye on this as it can quickly go from brown to burnt.
Once the butter has browned, transfer all of it to a large mixing bowl and allow it to come to room temperature. While it cools, grease a 9x5 loaf pan and preheat the oven to 325°F.
To the cooled butter, add both the white and brown sugar. Whisk well until thoroughly combined. Add the eggs and mix. Next add vanilla, mashed bananas and sour cream, and stir well until combined.
In a separate mixing bowl combine flour, baking powder, baking soda, cinnamon, and salt. Whisk well until well combined. Add the dry ingredients to the wet ingredients and mix just until no dry ingredients are visible in the batter.
Pour the batter into the greased loaf pan. Slice a banana lengthwise and lay it on top of the batter. If you're using the coarse sugar, sprinkle it on top right before baking. Bake in the oven for 45-48 mins, or until a toothpick inserted into the center comes out with a few crumbs.*
Let the banana bread sit in the loaf pan on a wire cooling rack for 15 minutes. Then gently loosen the edges with a dull knife (a plastic knife works great for this). Remove it from the pan and transfer it back to the wire rack to cool completely. Slice, serve, and enjoy!