Cut a pocket in each chop. Combine the next 10 ingredients. Reserve 1/2 cup for basting and refrigerate. Pour remaining marinade into a large resealable plastic bag or shallow glass container. Add pork and turn to coat. Seal bag or cover container; refrigerate overnight, turning meat occasionally.
Place a cheese slice on each slice of ham; roll up jelly-roll style. Drain pork and discard marinade in bag. Insert a ham/cheese roll in each pocket; secure with soaked toothpicks.
Grill, covered, over medium heat, for 4-5 minutes on each side or until a thermometer reads 145°, basting occasionally with reserved marinade. Let meat stand for 5 minutes before serving. Discard toothpicks.