In a large bowl, mix 2 cups flour, brown sugar, yeast, cinnamon, and salt.
Warm milk and butter until just melted and warm (not hot).
Add the milk mixture and mashed banana to the dry ingredients. Mix until combined.
Gradually add remaining flour and mix until a dough forms.
Knead on a floured surface for 8–10 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise for 1 hour until doubled.
Roll dough into a rectangle (about 18×12 inches).
Spread softened butter over the dough.
Mix brown sugar, cinnamon, and salt, then sprinkle evenly over the butter.
Roll tightly into a log and cut into 12 rolls.
Place in a lined baking dish and let rise again for 1 hour.
Bake at 350°F (175°C) for 25–30 minutes until golden.
Beat frosting ingredients until smooth and fluffy.
Spread frosting over warm banana bread cinnamon rolls and serve.