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 Ziploc® Fresh Shield® Double Zipper Storage 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. Insert a ham/cheese roll in each pocket; secure with soaked toothpicks.
Grill, covered, over medium heat, turning and basting occasionally with reserved marinade, for 25-35 minutes or until a meat thermometer reads 160°. Remove toothpicks.
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