Combine milk and butter in a glass measuring cup. Microwave for about 1 minute, or until milk is about 120 °F (49 °C)-130 °F (54 °C). Whisk melted butter into the milk to combine.
Add yeast to the bowl of your stand mixer. Pour in milk mixture. Gently stir and let sit 1 minute.
Add 3 cups flour, sugar, salt, and egg to the bowl. Using the paddle attachment, mix dough together until combined and starting to pull away from the sides of the bowl.
Add the other 3 tablespoons of flour and continue to mix until you have a thick dough that no longer sticks to the sides of the bowl.
Pour 1 tablespoon of vegetable oil into a clean bowl. Add the dough and swirl around to coat on all sides. Cover dough with a clean towel, set in a warm area, and let rise about 10 minutes.
Preheat oven to 350 °F (177 °C). Place 1 tablespoon (14g) butter in a 10-inch oven-safe skillet or pie dish. Place skillet in the oven and let butter melt 1 to 2 minutes. Remove skillet and swirl butter around to coat the bottom.
Roll dough onto a lightly floured surface until ¼ inch thick. Spread softened butter over top.
Combine sugar, apple pie spice, and cinnamon in a bowl. Sprinkle evenly on top of the butter.
Place chopped apple pie filling apples evenly on top of the dough.
Cut 9 long strips of dough and slowly roll each one tightly into a cinnamon roll shape, tucking the apples into the roll as needed.
Place rolls in the prepared skillet. Cover with a clean towel, and let rise another 10 minutes.
Bake cinnamon rolls for 28 to 35 minutes, or until lightly golden brown on top and baked through in the center.
Make Frosting
Beat cream cheese and butter on medium speed until smooth. Beat in powdered sugar. Once no lumps of sugar remain, add in milk, cinnamon, vanilla, and salt. Beat until smooth and creamy.
Frost tops of cinnamon rolls and serve while warm.