Prepare the tuna mixture: Combine drained tuna, mayonnaise, lemon juice, celery, red onion, parsley, Dijon mustard, garlic powder, salt, and pepper in a bowl.
Butter the bread: Spread softened butter on one side of each bread slice.
Build the sandwiches: Place four slices buttered-side down in a skillet. Add cheddar, tuna mixture, tomato, and mozzarella or provolone. Top with the remaining bread, buttered-side up.
Cook the first side: Cook over medium-low heat for 3 to 5 minutes, until the underside is golden and the cheese begins to melt.
Flip and finish: Turn the sandwiches carefully and cook until the second side is crisp and the cheese is fully melted. Rest for 2 minutes, then slice and serve.