In the bowl of a stand mixer, add 1 ½ cups of the flour and the yeast.
In a saucepan, heat the milk, ⅓ cup butter, sugar, and salt until 120 degrees F.
Remove the milk from the heat and stir until the butter is completely melted.
Use the regular paddle and start the mixer on low and mix the flour and yeast.
Slowly add the warmed milk to the flour and yeast.
Next, add the eggs one at a time.
Switch to the dough hook attachment, and continuing to beat on low, slowly add the remaining flour, a little at a time.
Increase speed to medium until a soft dough forms, approximately 3 minutes.
Transfer the dough to a lightly greased bowl, turning once to coat both sides. Cover with a clean dish towel.
Allow the dough to rise in a warm place until doubled, about 1 ½ hours.
Punch the dough down and turn out onto a lightly floured surface. Cover and allow to rest for 5 to 10 minutes.
Assembling the apple cinnamon rolls
Using a rolling pin, roll the dough into a 16 inch by 10 inch rectangle. If you roll the dough to thin, the apples will poke through the dough.
In a small bowl, mix the brown sugar, flour, and cinnamon.
Spread evenly with the butter, leaving a 1-inch space on one long edge without butter.
Spread the sugar cinnamon mixture evenly over the buttered dough, leaving the edge bare.
Over the brown sugar, place the apple pie filling into rows (making it easier to roll up the dough.)
Starting on the long side, roll the dough up, tucking the apple filling into each layer. Work the dough tightly but without pulling the dough too much. Seal the long edge by pinching it shut.
Cut the dough into 12 even slices by cutting the dough in half, cutting those halves in half and then the quarters into three slices each. Some of the apple mixture will leak out, but that's okay!
Place each roll in a 9 inch by 13 inch baking dish sprayed with nonstick cooking spray. Cover with plastic wrap or a clean towel, and allow to rise in a warm place for about 40 minutes or until doubled.
When the rolls have doubled in size, place the baking dish in a preheated oven and bake for 25 to 30 minutes.
Adding the cream cheese frosting
While the rolls bake, combine the cream cheese, butter, and vanilla, stirring until well blended. Stir in the powdered sugar and then add the milk a little at a time until reaching the desired consistency.
Remove rolls from the oven and spread or drizzle with the cream cheese icing.
Notes
For overnight apple cinnamon rolls, before allowing the final rise, the rolls may be tightly covered and placed in the refrigerator for up to 24 hours. Remove the rolls from the refrigerator the next morning and allow to rise before baking.