In a large bowl, warm the milk to 105-115°F. Dissolve the yeast in the warm milk, let it sit for 5 minutes until frothy.
Add the sugar, melted butter, and eggs to the bowl.
Gradually mix in 2 3/4 cups of flour to create a soft dough.
Knead the dough on a floured surface for about 10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let it rise for 1-1.5 hours in a warm place until doubled in size.
Roll the dough into a 16×12-inch rectangle on a floured surface.
Spread melted butter over the dough, then sprinkle with cinnamon and brown sugar.
Roll the dough tightly from the long end into a log and cut into 12-15 equal slices.
Place the rolls in a greased 9×13-inch baking dish, cover, and let them rise for another 30-60 minutes.
Preheat the oven to 375°F (190°C). Bake the rolls for 20-25 minutes or until golden brown.
While the rolls are baking, prepare the cream cheese icing: Beat the cream cheese until smooth. Mix in powdered sugar and milk until thick but spreadable. Stir in vanilla extract.
Once the rolls are baked, pour the warm icing over the top while the dish is still hot to create the sticky effect.
Let the icing set for a few minutes before serving.