Warm the whole milk and unsalted butter in a saucepan until butter is melted. Let it cool to lukewarm.

In a bowl, combine the warm milk mixture with active dry yeast and granulated sugar. Let sit for 10 minutes until foamy.

Add the egg, all-purpose flour, and salt. Mix and knead until the dough is smooth, about 5 minutes. Cover and let rise for 1 hour.

For the filling, mix the brown sugar, ground cinnamon, and softened butter into a paste.

Roll the dough into a 9x14-inch rectangle. Spread the filling evenly over the dough. Roll tightly and cut into 9 equal rolls.

Place the rolls in a greased 9x9-inch pan. Cover and let rise again for 30 minutes.

Preheat the oven to 350°F and bake for 22–25 minutes until golden.

Beat the cream cheese, softened butter, vanilla extract, and powdered sugar until smooth.

Spread the frosting over the warm rolls and serve.