Make the Banana Dough
Heat the milk to 110°F, then sprinkle the yeast over the top. Let it rest for 10 minutes until foamy.
In a large bowl, combine the flour, salt, and sugar. Add the cubed butter and knead with your hands or a pastry cutter until the butter is the size of peas.
Mix the yeast mixture, beaten egg, and mashed bananas into the dry ingredients. Use a mixer with a dough hook to knead the dough on low speed until it starts to form, then on medium speed for 5 minutes until smooth and elastic.
Spray a large bowl with nonstick spray. Place the dough in the bowl, cover it with a towel, and let it rise in a slightly warm oven (preheated to 200°F, then turned off) for about 1 hour until doubled in size.
Prepare the Cinnamon Banana Filling
Using a hand mixer, beat the butter on high speed until smooth. Add the brown sugar and cinnamon, mixing on medium speed for 1 minute until combined.
On a lightly floured surface, roll out the dough to a ¼-inch thick rectangle. Spread the filling evenly over the dough, then arrange the sliced bananas on top.
Assemble the Rolls
Roll the dough tightly from the shorter side to form a log. Use a serrated knife to trim the uneven ends and slice the log into 12 even rolls.
Spray a 9x13-inch baking dish with nonstick spray. Place the rolls in the dish, leaving space between them. Cover with a towel and let them rise for 20 minutes.
Bake the Rolls
Preheat your oven to 375°F.
Bake the rolls for 28–33 minutes, or until the tops are golden brown.
Make the Cream Cheese Icing
Beat the cream cheese and butter on high speed until smooth. Add the powdered sugar and vanilla, mixing on low speed until combined, then on high speed until fluffy.
Spread the icing over the warm rolls and serve.