In a small bowl, combine the warm milk, yeast, and granulated sugar. Let sit 5-10 minutes until frothy.
In a large mixing bowl, combine melted butter and egg. Add the frothy yeast mixture. Stir in flour and salt until soft dough forms, adding more flour if sticky.
Turn dough onto floured surface and knead 5-7 minutes until smooth and elastic. Place in greased bowl, cover with plastic wrap, and let rise 1 hour or until doubled.
While dough rises, mix brown sugar and cinnamon in a small bowl. Have softened butter ready.
Roll risen dough on floured surface into 1/4 inch thick rectangle.
Spread softened butter over dough, sprinkle cinnamon-sugar mixture evenly on top. Roll dough into tight log and pinch seams to seal.
Slice log into 12 equal pieces with a sharp knife or dental floss. Place rolls in greased baking dish.
Pour heavy cream evenly over the rolls to keep them moist while baking.
Preheat oven to 350°F (175°C). Bake rolls 25-30 minutes until golden brown and cooked through.
While rolls bake, prepare frosting by beating together softened cream cheese, softened butter, powdered sugar, and vanilla extract until smooth and creamy.
Let rolls cool a few minutes after baking. Spread cream cheese frosting generously on top. Serve warm and enjoy!