Activate the yeast. Heat the milk to about 110f using the method of your choice and then pour it into a large mixing bowl. Add the yeast along with two tablespoons of the sugar to the mixing bowl and allow the yeast to bloom (about 10 minutes).
Make the dough. Add the remaining sugar along with the butter and eggs to mixing bowl and mix until combined (a paddle attachment works fine). Then add half of the flour, mix and scrape down the sides of the bowl, and add the remaining flour. You can then switch to a dough hook and mix medium speed until a soft dough forms (about three minutes).
Rise. Form your dough into a large ball and then transfer it to a lightly greased bowl, turning once to coat both sides. Then cover the dough with a clean dish towel and allow it to rise doubled (about one and a half hours).
Punch the dough. Remove the dough from the bowl, place it onto a floured surface and then punch it down to relieve some of the air. Then cover the dough and allow to rest for 10 minutes.
Roll the dough . Use a rolling pin to roll your dough into a rectangle, approximately 20 inches by 10 inches. Then evenly spread the butter over the dough to about an inch from the edges.
Add the filling. In a medium bowl, use a whisk to mix together the brown sugar, flour, and apple pie spice. Then spread the mixture evenly over the buttered dough, leaving the edge bare. Over the brown sugar, use a spoon to evenly spread the apple pie filling, placing the apples into rows (horizontal on the dough)
Roll the dough. To roll up the dough, start with the wide side closest to you and roll the dough away from you, tucking the apple pie filling into each layer. You can seal the edge by pinching it shut.
Slice the dough. Prepare a casserole dish with nonstick. Then use a serrated knife to evenly slice the dough into 12 rolls before placing the rolls into the prepared baking dish. Cover the baking dish and allow the rolls to rise until doubled again (about 40 minutes).
Bake. Preheat your oven to 350 and bake your rolls for 25 to 30 minutes or until the edges begin to brown. While the rolls are cooling you can combined the remaining ingredients to make your icing.