Mash the ripe bananas until smooth in a large bowl.
Add eggs, sugar, melted butter, yeast, and warm milk. Mix until well combined.
Gradually add flour and salt. Knead until the dough is soft, smooth, and slightly sticky.
Place dough in a greased bowl, cover, and let rise until doubled, about 1 hour.
Mix butter, brown sugar, and cinnamon to make the filling. Set aside.
Roll dough into a large rectangle about ¼-inch thick.
Spread the cinnamon filling evenly over the dough.
Roll tightly into a log and slice into 12 even rolls.
Arrange rolls in a greased 9×13-inch baking dish.
Cover and let rise again until puffy, about 30–45 minutes.
Bake at 350°F (175°C) for 25–30 minutes, until golden brown.
Beat frosting ingredients until smooth and spread over warm rolls before serving.