Spread 0.5 tablespoons of butter on one side of each bread slice.
Place two bread slices butter-side down on a clean surface and spread 1 tablespoon of marinara sauce on the top side of each.
Distribute half of the shredded mozzarella cheese evenly over the marinara-covered slices.
Layer two slices of ham and one pineapple ring on top of the cheese on each sandwich base.
Sprinkle the remaining mozzarella and the grated parmesan over the pineapple.
Top with the remaining bread slices, butter-side facing outward.
Preheat a non-stick skillet over medium-low heat.
Place sandwiches in the skillet and cook for 4 minutes or until the bottom is golden brown.
Flip carefully and cook for an additional 3 to 4 minutes until the cheese is completely melted and the second side is toasted.
Remove from heat and let rest for 1 minute before slicing.