Drain water from tuna and put the tuna into a medium bowl.
Chop onion, celery, and parsley. Mince garlic and add ingredients to tuna.
Add mayonnaise, olive oil, and mozzarella cheese. Combine all ingredients until well incorporated. Salt and pepper to taste.
Place a non-stick skillet on the stove and add 1 tablespoon of olive oil. When the skillet is hot, take a slice of bread and generously spread butter on one side.
Place the bread (buttered side down) in the hot skillet.
Using a spoon, scoop about 2 tablespoons of tuna salad on bread while it is browning.
Butter another slice of bread with butter and place non-buttered side on top of tuna.
Using a spatula, check to see if the bread is toasted brown. If so, turn the tuna melt over and grill the other side until it's golden brown.