Preheat oven to 350°F (175°C).
Grease and flour a loaf pan.
Mash bananas thoroughly.
In a separate bowl, whisk together melted butter, sugars, eggs, and vanilla extract. Add the mashed bananas and mix until just combined.
In another bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Avoid overmixing.
In a small bowl, combine brown sugar, cinnamon, and a pinch of flour for the swirl.
Pour half of the banana bread batter into the loaf pan. Sprinkle the cinnamon swirl mixture evenly over the batter. Pour the remaining batter over the cinnamon swirl.
Use a knife or skewer to swirl the cinnamon mixture into the batter. Don’t over-swirl.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Let the banana bread cool in the loaf pan for 10-15 minutes before transferring it to a wire rack to cool completely.
Slice with a serrated knife and serve.