Prepare the Dough:

1. Heat milk to 110°F (warm to the touch). Sprinkle yeast over the milk and let sit for 10 minutes until foamy.
2. In a large bowl, whisk together flour, sugar, and salt.
3. Add cubed butter to the flour mixture and combine with your hands or a pastry cutter until it resembles coarse crumbs.
4. Add the yeast mixture, beaten egg, and mashed bananas. Knead with a stand mixer fitted with a dough hook for 5 minutes, or by hand for 8 minutes, until the dough is smooth and slightly sticky.

2. Let the Dough Rise:

1. Place the dough in a greased bowl, cover with a clean kitchen towel, and let rise in a warm spot for 1 hour or until doubled in size.

3. Make the Filling:

1. In a small bowl, mix softened butter, brown sugar, and cinnamon until combined.

4. Assemble the Rolls:

1. Roll the dough out on a floured surface into a rectangle about 1/4 inch thick.
2. Spread the cinnamon-sugar mixture evenly over the dough. Arrange thinly sliced bananas on top.
3. Roll the dough tightly into a log, starting from the short end. Cut into 12 even rolls using a serrated knife or unflavored dental floss.

5. Final Rise and Bake:

1. Place rolls in a greased 9×13-inch pan, leaving some space between each.
2. Cover and let rise for 20 minutes while preheating the oven to 375°F.
3. Bake for 28-33 minutes, or until golden brown.

6. Prepare the Icing:

1. In a mixing bowl, beat cream cheese and butter until smooth.
2. Add powdered sugar and vanilla, mixing until fluffy.

7. Ice and Serve:

1. Spread cream cheese icing over warm rolls, allowing it to melt slightly into the layers.
2. Serve immediately and enjoy the warm, gooey goodness.