In a large mixing bowl, combine warm milk, sugar, and yeast. Let sit for 5 minutes until foamy. Add melted butter, egg, salt, and flour. Knead for 8 minutes until smooth. Place in a greased bowl, cover, and let rise for 1 hour.
Mix together brown sugar and cinnamon. Roll out risen dough into a rectangle, spread softened butter on top, and sprinkle evenly with cinnamon sugar.
Roll the dough into a log from the long side. Slice into 12 even pieces using dental floss or a sharp knife. Place in a greased baking dish, cover, and let rise for 30-40 minutes.
Preheat oven to 350°F (180°C). Bake buns for 25-30 minutes until golden brown.
While buns bake, beat together cream cheese, butter, icing sugar, vanilla, and milk until smooth.
Spread the glaze over warm cinnamon buns. Serve immediately and enjoy!
Notes
For an overnight version, refrigerate sliced rolls overnight and bake in the morning after letting them rise at room temperature for 45 minutes.