Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
In a large bowl, combine the mashed bananas, granulated sugar, brown sugar, melted butter, egg, and vanilla extract. Mix until well combined.
In another bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the banana mixture, stirring until just combined. Do not overmix.
In a small bowl, mix together the brown sugar and cinnamon for the swirl. In another bowl, beat together the softened butter and the cinnamon sugar mixture until smooth.
Pour half of the banana bread batter into the prepared loaf pan. Spread half of the cinnamon swirl mixture over the batter. Pour the remaining batter on top and finish with the rest of the cinnamon swirl mixture. Use a knife to gently swirl the mixtures together.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Let it cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.
For the glaze, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Drizzle over the cooled banana bread rolls.