Preheat the oven to 350°F. Lightly coat a 9-by-5-inch loaf pan with nonstick cooking spray.
Add the mashed bananas, melted butter, granulated sugar, egg, and vanilla extract to a large mixing bowl. Stir until well combined.
Add the all-purpose flour, baking soda, and salt. Gently stir just until the dry ingredients disappear. Be careful not to overmix the batter.
In a small bowl, combine the brown sugar and cinnamon.
Pour half of the banana-bread batter into the prepared loaf pan and spread it into an even layer.
Sprinkle half of the brown sugar-cinnamon mixture evenly over the batter.
Pour the remaining banana batter into the pan. Sprinkle the rest of the cinnamon-sugar mixture over the top.
Run a butter knife or skewer gently through the batter a few times to create a swirl pattern.
Bake for approximately 60 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
While the bread is finishing, stir together the powdered sugar, vanilla extract, and milk until smooth.
Carefully remove the warm bread from the pan and place it on a wire cooling rack. Gently drizzle the vanilla icing over the top.
Allow the bread to cool completely before slicing—and enjoy!