Add the milk and egg to a large bowl and bring to room temperature.
Melt the butter in the microwave and add to the bowl. Add the sugar and mix with a fork.
Add the flour, salt, and instant yeast and mix together with your hands or a large spoon.
Form the dough into a ball and knead on a well floured surface for one to two minutes until the dough is elastic and smooth.
Place in a bowl sprayed with cooking spray, cover with plastic wrap, and leave in a warm place for 60 to 90 minutes. I'll often turn my oven for 1 minute, turn it right off, and then place the dough to rise in slightly warm oven. The dough will rise a bit, but not as much as regular bread dough, this is completely normal.
While the dough is rising, prepare the filling by mixing the brown sugar, butter, cinnamon, and nutmeg in a small bowl until smooth. Leave on the counter at room temperature.
Spray a 9” round pan with cooking spray.
Then roll the dough into an approximately 10”x16” rectangle on a well floured surface. Gently spread the cinnamon mixture on the dough with a butter knife or spreader.
Starting at the short end (the 10” end), roll the dough to form a tight roll.
Cut the roll into about 6 pieces and place in the baking dish. Cover lightly with plastic wrap sprayed with cooking spray and allow the rolls to rise for another 30 minutes.
Meanwhile, preheat the oven to 350 degrees Fahrenheit.
Bake for 20 to 25 minutes until the rolls are golden brown.
While the rolls are baking, prepare the frosting. Add the cream cheese and butter to a mixing bowl. Mix for about a minute until smooth and then gradually add the powdered sugar and vanilla extract and beat on medium low until fluffy and smooth. Refrigerate until ready to use.
As soon as you take the rolls out of the oven, spread half of the frosting on top as a glaze. Then add the remaining frosting a few minutes later and serve.