Warm milk to about 110℉. Combine warm milk and active dry yeast, allowing it to sit for about five minutes until foamy. In a large mixing bowl, whisk together mashed bananas, beaten egg, salt, white sugar, and cubed unsalted butter until well combined. Gradually add in the yeast mixture followed by all-purpose flour until a dough forms.
Transfer dough onto a floured surface and knead for about five minutes until smooth and elastic. Place in a greased bowl, cover with plastic wrap or a damp cloth, and let rise in a warm place for about an hour or until doubled in size.
Once risen, punch down the dough gently to release air bubbles. Roll it out on a floured surface into a rectangle shape about 1/4 inch thick.
Spread softened unsalted butter over the rolled-out dough evenly. Mix together brown sugar and ground cinnamon before sprinkling this mixture over the buttered dough. Top with thinly sliced bananas.
Starting from one long side of your rectangle, tightly roll up the dough into a log shape. Pinch seams together to seal it well. Cut into twelve equal pieces.
Place each roll in a greased baking dish close together so they touch slightly. Cover again and let them rise for another thirty minutes until slightly puffed up.
Preheat your oven to 350℉. Bake for about thirty minutes until golden brown on top.
While rolls are baking, beat together cream cheese and softened butter until smooth. Gradually add sifted powdered sugar and vanilla extract while mixing until creamy.
Once baked rolls have cooled slightly but are still warm, drizzle or spread generously with cream cheese icing over each roll before serving.