Warm the milk and melted butter together until the mixture reaches about 120–130°F (49–54°C). Stir in the granulated sugar and salt, then add the active dry yeast and let it stand for about 5 minutes until slightly foamy.

Beat in the eggs, then gradually mix in the flour until a soft dough forms. Knead for 3–5 minutes by hand or with a dough hook, adding only a little extra flour if necessary.

Cover the dough and let it rest for 10 minutes. This brief rest takes the place of the longer first rise used in traditional cinnamon-roll recipes.

Roll the dough into an approximately 15 x 20-inch rectangle. Spread it evenly with the softened butter, then sprinkle over the brown sugar and cinnamon.

Roll the dough tightly from the long side into a log. Cut the log into 12 evenly sized pieces using unflavored dental floss or a very sharp knife.

Arrange the rolls in a greased 9 x 13-inch baking pan. Let them rest for 5–10 minutes while the oven finishes heating to 375°F (190°C).

Bake for 12–16 minutes, until the rolls are puffed and lightly golden. Avoid overbaking so the centers remain soft and tender.

Beat the softened cream cheese and butter with the powdered sugar and vanilla. Add the milk gradually until the frosting reaches a smooth, spreadable consistency.

Wait about 5 minutes after baking, then spread the frosting over the warm rolls. Serve immediately while the centers are soft and the icing is creamy.