In a large mixing bowl, combine the warm milk, yeast, and a pinch of the granulated sugar. Let stand for 5 minutes until foamy and activated.
Add the remaining sugar, melted butter, and eggs to the yeast mixture. Whisk until well combined and slightly frothy.
Add 3 1/2 cups of flour and the salt. Mix with a wooden spoon or stand mixer with dough hook on low speed until a shaggy dough forms. Gradually add remaining flour until dough pulls away from the bowl sides but remains slightly tacky.
Knead the dough on a lightly floured surface for 8-10 minutes by hand (or 5-6 minutes in a stand mixer on medium speed) until smooth and elastic. Place in a greased bowl, cover with a damp towel, and let rise in a warm place for 1-1.5 hours until doubled in size.
While dough rises, mix the brown sugar and cinnamon in a small bowl. Prepare a 9x13-inch baking pan by greasing it generously with butter or lining with parchment paper.
Punch down the risen dough and turn out onto a floured surface. Roll into a 16x12-inch rectangle with even thickness throughout. Spread the softened butter evenly over the surface, leaving a 1/2-inch border on one long edge.
Sprinkle the cinnamon-sugar mixture evenly over the buttered dough. Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam to seal. Let rest for 5 minutes.
Using a sharp serrated knife or dental floss, cut the log into 12 equal rolls (about 1 1/3 inches each). Arrange cut-side up in the prepared pan with slight spacing between rolls. Cover and let rise for 30-45 minutes until puffy and nearly doubled.
Preheat oven to 350°F (175°C). Bake rolls for 25-30 minutes until golden brown on top and the internal temperature reaches 190°F. A toothpick inserted in the center should come out clean with no raw dough.
While rolls bake, beat the softened cream cheese and butter together until fluffy and smooth, about 2 minutes. Add the powdered sugar, lemon juice, and lemon zest. Beat on medium-high speed for 2-3 minutes until light and creamy. Spread frosting generously over rolls while they're still warm (not hot). Serve immediately or let cool completely.