Drain the water or oil from the tuna.
Place the tuna in a medium bowl and using a fork loosen it apart.
To the tuna bowl add the onion, celery, garlic, parsley, mayonnaise, 2 tablespoons olive oil, and mozzarella cheese. Stir to combine.
Salt and pepper to taste and mix again.
Place a nonstick skillet on the stove and add 1 tablespoon olive oil. Heat over medium heat.
Butter one side of a piece of bread and carefully place that slice butter side down into the now hot skillet.
Now spoon about 3 heaping tablespoons of tuna filling onto the slice of bread in the skillet, more or less depending on how thick you like your sandwiches.
Now take another slice of bread and butter one side. Place that slice of buttered bread on top of the sandwich in the skillet with the butter side up.
Watch for browning on the underside of the sandwich and grill until golden brown. Next flip the sandwich over and brown the other side.
Remove from the skillet and place on a paper towel lined plate.