Pre-heat a large skillet over medium heat. Add oil, then add enough ham slices to fill the pan. Brown ham for 2-3 minutes or until ham is browned. Flip ham slices and cook an additional 2-3 minutes. Transfer slices to a plate. Repeat with remaining ham slices. Set aside.
In the same pan, combine apple cider, brown sugar and mustard. Cook mixture over low heat until thickened slightly. Add ham slices back to pan and turn over slices to coat both sides with sauce. Remove pan from heat and set aside.
Place 1 slice of cheese on the bottoms of 4 rolls. Place 3-4 slices of reserved ham over cheese. Spoon coleslaw over ham. Place remaining cheese slices over slaw. Place bun tops over cheese. Serve.