Prepare Dough: In a bowl, mix yeast, warm milk, and sugar. Let sit for 10 minutes. In a large bowl, combine flour, mashed banana, egg, melted butter, and salt. Add yeast mixture, kneading until smooth. Cover and let rise for 1 hour.
Prepare Filling: Mix softened butter, brown sugar, and cinnamon in a small bowl.
Assemble Rolls: Roll out dough on a lightly floured surface into a rectangle. Spread filling evenly. Roll tightly and cut into 8 pieces.
Second Rise: Arrange rolls in a greased baking dish, cover, and let rise for 30 minutes.
Bake: Preheat oven to 350°F (175°C). Bake rolls for 20–25 minutes or until golden brown.
Make Icing: Beat together cream cheese, powdered sugar, vanilla, and milk until smooth. Spread over warm rolls.