Place the warm milk and yeast in a large mixing bowl. Let it sit for 10 minutes, until it starts to get foamy.
Add the sugar, butter, egg, egg yolk, and whisk to combine.
Add the flour and knead with electric mixer for 8 minutes. At this point, you should have a soft dough ball. If it is still quite sticky, add more flour, approximately 2 tablespoons at a time.
Transfer to a well-greased bowl and cover with a towel. Place in a warm area and let rise until doubled, about 1 ½ hours. I usually turn my oven on for a few minutes until it's warm, turn it off, and stick my dough in the slightly warm oven.
Once it has doubled in size, place it on a well-floured surface. Roll into a large rectangle that is approximately 10"x18".
Spread 3 tablespoons of the softened butter onto the rectangle, and then sprinkle with 2 tablespoons o brown sugar.
In a small skillet, add the remaining 2 tablespoons of butter, shredded apple, cinnamon, and nutmeg. Saute until the apple is softened, about 5 minutes.
Sprinkle the apple over the dough.
Roll the dough tightly so you have one long roll. Cut the roll into half, then into quarters. Cut each quarter into 3 even cinnamon rolls so you have 12 rolls total.
Place the cinnamon rolls into a greased 9x13" baking dish.
Cover with a towel and let it sit at room temperature for 30-45 minutes, until rolls have risen.
Preheat the oven to 350 degrees F.
Bake the cinnamon rolls for 25-30 minutes, until golden on top.
Make the caramel cream cheese frosting by beating cream cheese, butter, and caramel sauce in a bowl with electric mixer until combined.
Spread the frosting over the warm cinnamon rolls.
Serve and enjoy!