In a small bowl combine the melted butter, white sugar, brown sugar, cinnamon, and nutmeg. Stir to combine, set aside.
For the banana bread:
Preheat oven to 350°F. Lightly grease or line a loaf pan and set aside.
In a large bowl, melt the butter and let cool slightly. Add in the sugar and whisk until dissolved. Mix in the vanilla and the eggs, one at a time.
In a small bowl combine the flour, baking soda, and salt. Stir to combine. Gently mix the flour mixture into the wet ingredients. Fold in the mashed bananas.
Scoop half of the batter into the prepared loaf pan, sprinkle half of the cinnamon sugar mixture evenly over the first layer. Using a toothpick or a butter knife gently swirl the cinnamon mix into the batter. Spread the remaining batter on top and top with the rest of the cinnamon sugar mix. Again swirling it in.
Bake for 55-60 minutes, or until a toothpick comes out clean. Let the bread cool in the loaf pan for 20-30 minutes, before removing. Slice and enjoy.