In a large bowl, combine 2 cups of flour, brown sugar, yeast, cinnamon, and salt, and mix to combine.
In a microwave-safe bowl, warm the milk and butter together for about 30 seconds until the butter is mostly melted and the mixture is warm but not hot.
If it's too hot, let it cool before adding to the flour mixture to avoid killing the yeast.
Add the warm milk mixture and mashed banana to the dry ingredients and beat on low speed, increasing to high until fully incorporated, about 2 minutes.
Scrape the sides of the bowl, then add another cup of flour and beat until combined.
Gradually add the remaining cup of flour until the dough pulls away from the sides and forms a ball.
Turn the dough onto a well-floured surface and knead for about 10 minutes until smooth and stretchy.
Transfer the dough to an oiled bowl, cover, and let rise in a warm place for 1 hour, or until doubled in size.
While the dough rises, mix the brown sugar, cinnamon, and salt for the filling in a small bowl and set aside.
Once risen, roll the dough into an 18x12 inch rectangle on a floured surface.
Spread softened butter all over the surface of the dough, then sprinkle the cinnamon sugar mixture evenly on top, pressing gently so it adheres.
Roll the dough tightly from the long edge and pinch the seam to seal.
Slice into 12 even rolls using floss or a sharp knife, then place them in a parchment-lined 9x13 inch pan.
Cover loosely and let rise again for about 1 hour, or until puffed and doubled.
Bake at 350°F for 30 minutes until golden brown and fully baked.
Let the rolls cool slightly while you prepare the cream cheese frosting by beating the cream cheese, butter, powdered sugar, milk, salt, and vanilla extract together until fluffy.
Spread the frosting over the warm rolls and enjoy.