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

Add melted butter, egg, salt, and flour. Mix until a dough forms.

Knead the dough on a floured surface for about 5 minutes until smooth.

Place the dough in a greased bowl, cover, and let it rise in a warm place for 1 hour or until doubled in size.

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

Preheat the oven to 350°F (175°C).

Roll out the dough on a floured surface into a rectangle about 1/4 inch thick.

Spread the banana filling evenly over the dough.

Roll the dough tightly from one end to the other and cut into 1-inch thick rolls.

Place the rolls on a greased baking sheet and let them rise for another 30 minutes.

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

In a bowl, whisk together powdered sugar, milk, and vanilla extract until smooth.

Drizzle the glaze over the warm rolls and serve immediately.