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.
Preheat oven to 350 degrees. Line a muffin tin with liners or lightly grease.
Punch down the dough and roll into a 12inch by 20inch rectangle.
Spread the softened butter out over the dough In a small bowl, combine the brown sugar and cinnamon. Sprinkle on top of the butter. Roll up tightly lengthwise so you have one long roll. Use a sharp knife to cut the dough into 18 slices (1 inch) slices
Bake the cupcake rolls for about 15 minutes, until just kissed with brown on top.
While the cinnamon rolls are baking, make the cream cheese frosting by using a hand mixer to whip together cream cheese, butter and vanilla extract in a bowl until light and fluffy. Whip in powdered sugar 1/2 cup at a time until thickened.
Frost the rolls once cooled. Serve immediately or cool and store. Stays good for 4 to 5 days.