In a microwave safe bowl, combine the cubed butter, milk, and butter. Heat on high in 30-second increments until warm and the butter is melted. NOTE: the mixture should be warm to the touch, not hot. If it is too hot, let it sit for a few minutes to cool before adding to the flour mixture.
In the bowl of a stand mixer, combine 3 cups of the flour, granulated sugar, powdered milk, yeast, and salt. Add the warmed milk/butter mixture and the egg and mix until combined with the dough hook attachment. Continue to knead the dough with the dough hook for 5 minutes, adding up to 3/4 cup of the remaining flour as needed until the dough is soft and pulls away from the sides of the bowl to form a ball. Cover the dough and let rest for 15 minutes.
Roll the dough out on a floured surface into a 10x14-inch rectangle. Spread the softened butter onto the dough.
In a small bowl, combine the brown sugar, cinnamon, and nutmeg. Sprinkle this over the butter on the dough.
Top the cinnamon/sugar mixture with the diced apples and then drizzle with 1/3 cup of the caramel sauce.
Beginning at one of the short ends of the dough, roll from one end to the other like a jelly roll. Cut the roll into 12 individual cinnamon rolls. Place the rolls into a 9x13-inch baking dish that has been greased with non-stick cooking spray.
Cover the rolls lightly with a clean kitchen towel and place in a warm location to rise for 30 minutes. While the rolls are rising, preheat the oven to 350F.
Bake the rolls at 350F for 15-18 minutes until golden brown. Drizzle with the remaining 1/3 cup of caramel sauce while hot. Allow the rolls to cool in the pan for 10 minutes, then serve warm.