1Make the dough by combining the warm milk (around 110°F - warm to the touch but not hot), melted butter, granulated sugar, and eggs in a large mixing bowl. Whisk together until well combined. In a separate bowl, whisk together the flour, instant yeast, and salt. Gradually add the dry ingredients to the wet ingredients, mixing with a wooden spoon or stand mixer fitted with a dough hook on low speed. Mix until a shaggy dough forms, then knead for 6-8 minutes by hand on a floured surface or with the dough hook on medium speed until the dough is smooth, elastic, and slightly tacky but not sticky. If the dough is too sticky, add flour one tablespoon at a time. If too dry, add milk one teaspoon at a time. The dough should spring back when poked and hold its shape.
2Place the kneaded dough in a greased bowl, turning it once to coat all sides with oil or butter. Cover the bowl with a clean kitchen towel or plastic wrap and let it rise in a warm, draft-free location for about 1 to 1.5 hours, or until doubled in size. A good spot is near a warm oven or in a slightly warmed oven (turn it on to the lowest setting for 1 minute, then turn it off). The dough is ready when you press two fingers into it and the indentations remain. While the dough rises, prepare your filling by mixing the brown sugar and cinnamon together in a small bowl until well combined. Have your softened butter ready for spreading.
3Once the dough has doubled, punch it down gently to release the air. Turn it out onto a lightly floured surface and roll it into a large rectangle, approximately 16x12 inches. The dough should be about 1/4 inch thick. Try to keep the edges as straight as possible for even rolls. Spread the softened butter evenly over the entire surface of the dough, leaving a 1/2-inch border along one of the long edges (this will be your sealing edge). Sprinkle the cinnamon-sugar mixture generously and evenly over the buttered dough, using your hands to press it gently into the butter so it adheres well.
4Starting from the long edge opposite the border you left, tightly roll the dough into a log, keeping the roll as even and tight as possible without squeezing out the filling. A tight roll ensures beautiful swirls and prevents gaps in your finished rolls. When you reach the end, pinch the seam to seal it closed. Using a sharp knife or unflavored dental floss (slide it under the log, cross the ends over the top, and pull to slice cleanly), cut the log into 12 equal pieces, each about 1.5 inches thick. For the most uniform rolls, mark the log into quarters first, then cut each quarter into three pieces. Place the rolls cut-side up in a greased 9x13 inch baking pan, spacing them slightly apart. They will expand and touch during the second rise and baking, creating those signature soft, pull-apart edges.
5Cover the pan with a towel and let the rolls rise again for 30-45 minutes in a warm place until puffy and nearly doubled in size. They should look pillowy and fill most of the pan. While they rise, preheat your oven to 350°F (175°C). Once risen, bake the uncovered rolls for 20-25 minutes until they are golden brown on top and cooked through. The internal temperature should reach about 190°F if you have a thermometer. The rolls should be soft and springy to the touch, with golden edges and a slightly darker top. Remove from the oven and let them cool in the pan for about 10 minutes while you prepare the frosting.
6Make the cream cheese frosting by beating together the softened cream cheese and butter in a medium bowl with an electric mixer on medium speed until smooth and creamy, about 2 minutes. The mixture should be completely combined with no lumps. Add the powdered sugar, vanilla extract, and milk, then beat on low speed until incorporated, then increase to medium-high speed and beat for another 2-3 minutes until light and fluffy. The frosting should be smooth, spreadable, and slightly thick. If too thick, add more milk one teaspoon at a time; if too thin, add more powdered sugar. Generously spread or pipe the frosting over the warm (not hot) cinnamon rolls. The warmth will cause the frosting to melt slightly into the rolls, creating an irresistibly gooey, sweet topping. Serve immediately while warm for the ultimate cinnamon roll experience.