In a large bowl, combine warm milk, active dry yeast, egg, melted butter, granulated sugar, and salt. Whisk until smoothly blended, then gradually add all-purpose flour until a soft dough forms. Knead for 3 minutes until slightly tacky, then cover and let rise for 1 hour until doubled.

Mix together softened butter, brown sugar, and ground cinnamon in a small bowl until fully incorporated. Set aside while the dough rises.

Turn the risen dough onto a floured surface and roll it into a 12x18 inch rectangle. Spread the cinnamon filling evenly, leaving a small border. Roll tightly lengthwise into a log and cut into 8 equal pieces. Arrange in a greased baking pan.

Cover with a towel and let rise for an additional 30 minutes. Preheat the oven to 350°F.

Brush the rolls with remaining melted butter and bake for 20-25 minutes until golden brown.

Allow to cool slightly, then beat together softened butter, cream cheese, vanilla extract, and powdered sugar until creamy. Spread over warm rolls.