Put all the dough ingredients into your bread machine in the order recommended by the manufacturer and set on the dough setting.
Allow to rise in the machine* for 1-2 hours once the cycle finishes, or until doubled in size.
Punch dough down and roll it out into a long 1/4" thick rectangle. Brush with melted butter and sprinkle with sugar, brown sugar, and cinnamon. Spoon apple pie filling in an even layer over the dough leaving about 1 inch of space on all sides to allow for spreading as you roll.
Roll dough tight, trying to keep the filling from squeezing out, and pinch the seam closed. Cut dough in half and repeat with each section until you have 8 equal sized rolls.
Lay cut rolls in a greased or lined baking dish and cover with a clean dish towel. Allow to rise for an hour until doubled in size.
Bake at 350 degrees for 25-30 minutes or until golden brown.
While the rolls are baking prepare the icing, using milk to reach your desired thickness.
Ice rolls while still warm but not hot and serve warm.