Step 1: In the bowl of a stand mixer, combine the warm milk, yeast, and 1 tablespoon of the granulated sugar. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.
Step 2: Add the remaining granulated sugar, melted butter, eggs, and salt to the yeast mixture. Mix until well combined.
Step 3: Gradually add the all-purpose flour, 1 cup at a time, mixing on low speed with the dough hook until a shaggy dough forms. Increase speed to medium-low and knead for 5-7 minutes, until the dough is smooth and elastic. It should be slightly sticky but pull away from the sides of the bowl.
Step 4: Lightly grease a large bowl with oil. Place the dough in the bowl, turning once to coat. Cover with plastic wrap or a clean kitchen towel and let rise in a warm, draft-free place for 1 to 1.5 hours, or until doubled in size.
Step 5: While the dough is rising, prepare the filling. In a small bowl, combine the softened butter, brown sugar, and ground cinnamon until well mixed and spreadable.
Step 6: Once the dough has doubled, gently punch it down to release the air. Transfer the dough to a lightly floured surface and roll it into a large rectangle, approximately 12x18 inches.
Step 7: Evenly spread the cinnamon-sugar filling over the entire surface of the dough, leaving a small border (about 1/2 inch) on one of the long edges clean.
Step 8: Starting from the long edge opposite the clean border, tightly roll the dough into a log. Pinch the seam gently to seal.
Step 9: Using a sharp knife or unflavored dental floss, cut the log into 12 even slices, about 1.5 inches thick. Arrange the slices in a lightly greased 9x13 inch baking dish.
Step 10: Cover the baking dish with plastic wrap or a kitchen towel and let the rolls rise again in a warm place for another 45-60 minutes, or until they look puffy and have nearly doubled in size.
Step 11: Preheat your oven to 375°F (190°C). Bake the cinnamon rolls for 20-25 minutes, or until they are golden brown on top and cooked through. If they start browning too quickly, you can loosely tent them with foil.
Step 12: While the rolls are baking, prepare the cream cheese frosting. In a medium bowl, beat the softened cream cheese and butter with an electric mixer until smooth and creamy. Gradually add the powdered sugar, mixing until well combined. Stir in the vanilla extract and 1 tablespoon of milk. Add more milk, if needed, to reach your desired consistency.
Step 13: Once the cinnamon rolls are out of the oven, let them cool for 5-10 minutes before spreading generously with the cream cheese frosting. Serve warm and enjoy!