Place skillet on the burner and set heat to medium-low.
On 4 slices of bread, spread ½ tablespoon of butter on east side of the bread. Place 2 slices of bread butter side down in skillet. Spread 1 tablespoon of pizza sauce onto each slice of bread in the skillet. Next, layer 2 tablespoon of shredded cheese to each slice in the skillet.
Next, ham, pineapple, and remaining mozzarella. Top with 1 tablespoon of pizza sauce. Top with remaining 2 slices of bread.
Cook sandwiches until golden brown on the bottom, about 3-4 minutes. Flip sandwiches and cook until golden brown on the other side and the cheese has fully melted, about 3-4 remaining minutes. If the bread turns golden brown before the cheese has fully melted, reduced stove heat to low. Remove from heat and enjoy!