Preheat the oven to 350°F and lightly grease a 9x5 inch loaf pan.
In a large bowl, whisk together flour, baking soda, and salt.
In another bowl, stir together melted butter and brown sugar until smooth. Add eggs and mashed bananas, mixing well.
Combine the wet and dry ingredients just until blended.
In a small bowl, mix granulated sugar and cinnamon to make the swirl mixture.
Pour half of the batter into the prepared pan, sprinkle half the cinnamon-sugar over it, then repeat with the remaining batter and cinnamon-sugar.
Use a knife to gently swirl the cinnamon mixture through the batter.
Bake for 60 minutes or until a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.