In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until frothy.

Add the beaten egg, melted butter, and salt to the mixture. Gradually stir in the flour until a dough forms.

Knead the dough on a floured surface for about 5 minutes until smooth. Place in a greased bowl, cover, and let rise for 1 hour.

In a separate bowl, mix the mashed bananas, brown sugar, cinnamon, and softened butter until well combined.

Preheat the oven to 350°F (175°C). Roll out the dough into a rectangle on a floured surface.

Spread the banana filling evenly over the dough, then roll it tightly into a log.

Cut the log into 1-inch thick slices and place them in a greased baking dish. Let them rise for another 30 minutes.

Bake the rolls in the preheated oven for 20-25 minutes until golden brown.

While the rolls are baking, whisk together the powdered sugar, milk, and vanilla extract to make the glaze.

Once the rolls are done, drizzle the glaze over them while they are still warm.