In a small bowl, dissolve yeast in warm water and let bloom. Set aside.
In a large bowl, combine milk, sugar, melted butter, salt and beaten egg. Add 2 cups of flour and mix until smooth. Add yeast mixture. Mix in remaining flour until dough is easy to handle. Knead dough on lightly floured surface for 5 minutes. Place in well-greased bowl, cover with a damp dish cloth and let rise until doubled in size, about 1 to 1½ hours depending on the environment.
While the dough is rising, make the filling by combining the brown sugar, cinnamon and butter in a bowl. Set aside. Make the cream cheese icing by combining the butter, icing sugar, cream cheese and vanilla. Set aside.
When the dough has finished doubling in size, punch down the dough. Roll out on a floured surface into a 15 by 9-inch rectangle. Spread the filling evenly over the surface of the dough.
Beginning at the long side, roll up the dough into long log. Cut into 12 equal pieces and arrange into a greased 9x13-inch baking pan. Cover with a damp dish cloth and let rise for another 30 minutes. While rising, preheat oven to 350 °F.
Bake the rolls for 25- 30 minutes or until lightly browned. Let rest for 3-5 minutes. Spread the cream cheese icing over the warm cinnamon rolls.