In a large mixing bowl, combine 2 cups of the all-purpose flour with the packed brown sugar, rapid-rise yeast, ground cinnamon, and salt. Stir everything together until evenly mixed.
In a separate microwave-safe bowl, heat the milk and butter together for about 30 seconds until the mixture is warm and the butter is mostly melted. The temperature should be warm but not hot—if it feels too hot, let it cool slightly before adding to avoid deactivating the yeast. Pour the warm milk-butter mixture and the mashed banana into the bowl with the dry ingredients.
Using a mixer on low speed, begin blending the ingredients, gradually increasing the speed to high. Beat for about 2 minutes, or until fully incorporated.
Scrape down the sides of the bowl and add in 1 additional cup of flour. Continue mixing until well combined. Gradually add the remaining 1 cup of flour, mixing in a bit at a time until the dough pulls away from the sides of the bowl and starts forming a cohesive ball.
Transfer the dough to a floured surface and knead it by hand for approximately 10 minutes, or until it becomes smooth and elastic. You should be able to gently stretch a small piece between your fingers without it tearing—this indicates the gluten has developed properly.
Place the kneaded dough in a lightly oiled bowl, cover with a clean towel or plastic wrap, and let it rise in a warm place for about 1 hour, or until it has doubled in size.
While the dough is rising, prepare the filling by mixing the brown sugar, cinnamon, and a pinch of salt together in a small bowl. Set the mixture aside.
Once the dough has finished rising, roll it out on a floured surface into a large rectangle measuring about 18 by 12 inches.
Spread the softened butter for the filling evenly over the entire surface of the dough, making sure to reach the edges. Evenly sprinkle the prepared sugar mixture over the butter layer, gently pressing it down so it adheres well.
Starting with the long edge, tightly roll the dough into a log, then pinch the seam along the bottom to seal it closed.
Using unflavored dental floss or a very sharp knife, slice the dough log into 12 equal pieces. Arrange the rolls cut-side up in a parchment-lined 9 x 13-inch baking dish. Cover loosely with a clean dish towel and allow them to rise again for about an hour, or until they’ve doubled in size and look puffy.
Preheat the oven to 350°F (175°C). Bake the cinnamon rolls for approximately 30 minutes, or until they’re golden brown and baked through. Allow the rolls to cool slightly in the pan.
While the rolls are cooling, prepare the cinnamon cream cheese frosting. In a stand mixer fitted with a whisk attachment, beat together the cream cheese, softened butter, powdered sugar, milk, salt, and vanilla extract. Start on low speed, gradually increasing to high, and mix until the frosting is smooth, fluffy, and light.
Spread the frosting evenly over the warm rolls and enjoy them fresh!