In the bowl of a stand mixer, combine warm milk, yeast, sugar, salt, butter, and egg. Add in flour. Using a dough hook, turn the mixer on to a low speed.
Once the flour starts to incorporate into the dough, increase the speed to a medium range. Add more flour as necessary so that the dough pulls away from the sides of the bowl. The dough mixture should be tacky, but not stick to your hands. It should be soft. Add more or less flour until the dough reaches the desired consistency. The amount of flour you add in bread making is always an approximation and you should go by feel.
Transfer the dough to a lightly greased mixing bowl. Cover with a towel and let rise until double in size, about 1 hour.
Lightly grease a baking sheet. Punch down the dough and roll into a 12x18 inch rectangle.
Brush the dough with 1/2 cup melted butter. In a small bowl, combine brown sugar and cinnamon. Sprinkle on top of the melted butter. Roll up tightly lengthwise so you have one long roll. Use plain dental floss or a sharp knife to cut the dough into 12 one-inch slices.
Places slices onto a lightly greased 9x13 pan. Cover and let rise 30-45 minutes.
Preheat oven to 325º. Bake the rolls for about 14 minutes, until just kissed with brown on top.
While the cinnamon rolls are baking, make the cream cheese glaze by using a hand mixer to whip together cream cheese and butter in a bowl until light and fluffy. Whip in powdered sugar and vanilla extract. Add enough milk to achieve a drizzle-like consistency.
Frost the rolls while still warm. Serve immediately or cool and store. Stays good for 4 to 5 days.