In a large mixing bowl, combine the flour, granulated sugar, instant yeast, and salt and whisk to blend.
In a separate bowl, whisk together the warm milk, mashed bananas, melted butter, and egg until smooth.
Pour the wet ingredients into the dry ingredients and mix with a wooden spoon or dough hook until a soft, shaggy dough forms.
Turn the dough onto a lightly floured surface and knead for 8 to 10 minutes until smooth, soft, and elastic, adding small amounts of flour only as needed to prevent sticking.
Place the dough in a greased bowl, turn once to coat, cover with a clean kitchen towel, and let rise in a warm place for 60 to 90 minutes or until doubled in size.
In a small bowl, stir together the brown sugar and ground cinnamon for the filling and set aside.
Punch down the risen dough and turn it out onto a lightly floured surface, then roll it into a large rectangle about 1/4 inch thick.
Spread the 3 tablespoons of softened butter evenly over the surface of the dough, all the way to the edges.
Sprinkle the brown sugar and cinnamon mixture evenly over the buttered dough, pressing it lightly so it adheres.
Starting from a long side, roll the dough up tightly into a log, pinching the seam to seal.
Using a sharp knife or unflavored dental floss, cut the log into 9 equal rolls.
Arrange the rolls, cut side up, in a greased 9x13-inch baking dish, leaving a little space between each roll.
Cover the pan and let the rolls rise in a warm place for 30 to 45 minutes, or until puffy and nearly doubled.
Preheat the oven to 350°F while the rolls finish their second rise.
Bake the rolls for 25 minutes, or until golden brown on top and they sound hollow when tapped lightly.
While the rolls bake, beat the softened cream cheese and 1/4 cup softened butter together in a mixing bowl until smooth and creamy.
Add the powdered sugar and vanilla bean paste to the cream cheese mixture and beat until thick, smooth, and fluffy.
Remove the rolls from the oven and let them cool in the pan for 5 to 10 minutes.
Spread the cream cheese frosting generously over the warm rolls so it melts slightly into the swirls.
Serve the Banana Bread Cinnamon Rolls with Cream Cheese Frosting warm and enjoy.