In a large mixing bowl, whisk together flour, sugar, yeast, and salt. In another bowl, mix warm milk, mashed bananas, melted butter, and egg until smooth. Gradually combine wet and dry ingredients to form dough.

Transfer the dough to a floured surface and knead for 8-10 minutes until smooth and elastic. Grease a bowl, place the dough inside, cover with plastic wrap, and let rise in a warm spot for 60-90 minutes.

Roll the dough out onto a floured surface into a rectangle, about 12x18 inches.

Spread softened butter over the rolled-out dough. Mix brown sugar and cinnamon, and sprinkle evenly over the buttered dough.

Roll the dough tightly from one edge into a log. Cut the log into 9 equal pieces.

Place sliced rolls into a greased baking dish, cover with a towel, and let rise for 30-45 minutes.

Preheat the oven to 350°F (175°C). Bake rolls for 25-30 minutes until golden brown.

While baking, prepare the frosting by mixing cream cheese, softened butter, powdered sugar, and vanilla extract until smooth.

Spread frosting over the warm rolls before serving.