Preheat the oven to 350° and spray a 9x13 inch pan with nonstick cooking spray.
Cut the Hawaiian rolls in half and place the bottom half in the pan.
Lay the ham over the bottom of the rolls.
Heat a grill pan or cast iron pan over medium high heat. In a small bowl, combine the pineapple juice, brown sugar, soy sauce, ginger, and garlic. Brush over the pineapple slices and place in the hot pan. Keep the remaining sauce for brushing over the top buns. Grill each side for 1 minute or until it has grill marks.
Cut the rings in half and lay over the ham.
Layer the cheese over the pineapple.
Place the top buns over the pineapple.
Add the melted butter and parsley to the remaining marinade. Brush over the tops of the buns.
Tent a piece of tinfoil over the rolls and place in the oven. Bake for 15 to 20 minutes until cheese is melted. Remove the tinfoil and bake an additional 5 minutes until lightly browned.