Combine warm milk with one teaspoon of sugar and the dried yeast. Stir gently and let the mixture sit for about 5 minutes until it becomes foamy.
In a large bowl, mix the flour, sugar, salt, melted butter, and egg. Gradually pour in the milk and yeast mixture while kneading on low speed. Continue kneading for about 10 minutes until the dough turns smooth and elastic.
Lightly grease the bowl, place the dough inside, and cover it with plastic wrap or a clean towel. Let it rise in a warm place for about 1 hour or until it doubles in size.
Dust your work surface with flour and roll the dough into a rectangle, about 15 x 9 inches. Spread the softened butter evenly over the surface, leaving a ¼-inch margin at the edges.
Add the filling: Mix the brown sugar and cinnamon in a small bowl. Sprinkle the mixture evenly over the buttered dough.
Shape the rolls: Starting from the long side, roll the dough tightly like a jelly roll. Trim about an inch from each end to remove uneven edges. Slice the roll into 12 equal pieces.
Arrange the slices in a greased 13 x 9-inch baking dish. Cover with plastic wrap and let them rise again for 30–45 minutes until puffy.
Preheat the oven to 180°C (350°F). Brush the tops with melted butter and bake for about 25–30 minutes, or until golden brown. Let it cool fo 10 minutes.
Whisk together the cream cheese, powdered sugar, vanilla, and milk until smooth and creamy.
Drizzle the warm rolls generously with the cream cheese frosting. Serve immediately and enjoy the irresistible aroma and taste of fresh homemade cinnamon rolls!