Step 1: In a large bowl, combine the warm milk, yeast, and 1 tablespoon of the granulated sugar. Stir gently and let it sit for 5-10 minutes until foamy.
Step 2: Add the remaining granulated sugar, mashed bananas, egg, salt, and melted butter to the yeast mixture. Whisk until well combined.
Step 3: Gradually add the flour, 1 cup at a time, mixing with a wooden spoon or stand mixer until a shaggy dough forms.
Step 4: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or use a stand mixer with a dough hook for 3-5 minutes, until the dough is smooth and elastic. It should be slightly sticky but manageable.
Step 5: Place the dough in a lightly greased bowl, turning once to coat. Cover with plastic wrap and let rise in a warm place for 1-1.5 hours, or until doubled in size.
Step 6: While the dough is rising, prepare the filling. In a small bowl, cream together the softened butter, brown sugar, and cinnamon until well combined.
Step 7: Once the dough has risen, punch it down gently. On a lightly floured surface, roll the dough into a large rectangle, approximately 12x18 inches.
Step 8: Spread the cinnamon-sugar filling evenly over the dough, leaving a small border on one long edge.
Step 9: Starting from the long edge opposite the border, carefully roll the dough into a tight log. Use a sharp chef's knife or unflavored dental floss to slice the log into 12 equal rolls, about 1.5 inches thick.
Step 10: Arrange the rolls in a lightly greased 9x13 inch baking dish, leaving a little space between each. Cover loosely with plastic wrap and let rise again in a warm place for 30-45 minutes, or until puffy.
Step 11: Preheat your oven to 375°F (190°C). Bake the rolls for 20-25 minutes, or until golden brown and cooked through. If they start to brown too quickly, you can loosely tent them with foil.
Step 12: While the rolls are baking, prepare the cream cheese glaze. In a medium bowl, beat the softened cream cheese and butter together until smooth. Gradually add the powdered sugar, milk, and vanilla extract, beating until light and fluffy.
Step 13: Once the rolls are out of the oven, let them cool for 5-10 minutes before generously drizzling with the cream cheese glaze. Serve warm.