In a bowl, combine warm milk, yeast, granulated sugar, melted butter, salt, and egg. Stir until yeast dissolves.
Gradually add flour, stirring until dough begins to form. If dough sticks too much, add a little more flour until it’s soft but not dry.
Knead dough about 5–7 minutes until smooth and elastic. Place in a lightly greased bowl, cover, and let rise in a warm spot until doubled in size (~1 hour).
On a floured surface, roll dough into a rectangle (about 12 × 18 in). Spread softened butter evenly over dough.
Mix brown sugar + cinnamon then sprinkle evenly over buttered dough. Roll tightly from the long side into a log. Pinch seam to seal.
Cut log into 12 rolls (about 1–1.5 in slices) and place them cut-side up in a greased 9×13 pan. Cover and let rise for 30–45 minutes until puffy.
Preheat oven to 350 °F (175 °C). Bake rolls for 20–25 minutes or until golden brown. Let cool slightly.
For glaze: beat cream cheese and butter until smooth, gradually add powdered sugar, vanilla, and milk. Drizzle over warm rolls. Serve warm.