Make the Dough : In a small bowl, combine the warm milk and yeast. Let it sit for 5-10 minutes until frothy. In a large mixing bowl, combine the beaten egg, mashed bananas, flour, salt, and sugar. Add the yeast mixture and mix until a dough forms. Knead the dough on a floured surface for 8-10 minutes, or use a stand mixer with a dough hook for 5-7 minutes, until the dough is smooth and elastic. Gradually add the cubed butter, a few pieces at a time, kneading until fully incorporated. Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm spot for 1-2 hours, or until it doubles in size.
Prepare the Filling : In a small bowl, mix the softened butter, brown sugar, and ground cinnamon until well combined.
Assemble the Rolls : Roll out the dough on a floured surface into a large rectangle (approximately 12x18 inches). Spread the cinnamon-sugar mixture evenly over the dough. Arrange the banana slices on top. Roll the dough tightly from the longer side to form a log. Slice into 12 equal pieces. Place the rolls in a greased 9x13-inch baking dish, cover, and let rise for 30-45 minutes.
Bake the Rolls : Preheat the oven to 350°F (175°C). Bake the rolls for 25-30 minutes, or until golden brown. Let cool slightly before adding icing.
Make the Cream Cheese Icing : Beat the cream cheese and butter until smooth. Gradually add the powdered sugar, mixing until creamy. Stir in the vanilla extract.
Frost and Serve : Spread the cream cheese icing generously over the warm rolls. Serve immediately and enjoy!