Place the tuna in a medium mixing bowl and break it apart with a fork. Add the green onion, celery, mayo, salt, pepper, and Mozzarella to the tuna and mix well. Refrigerate the tuna mixture until needed.
Heat oven’s broiler. Line a baking sheet with aluminum foil.
Spread the butter generously over both sides of each piece of bread.
Place the bread on the prepared baking sheet and broil the bread until golden brown on top, about 2-3 minutes. Flip each slice of bread over and continue to broil until the second side is toasted, an additional 2-3 minutes. Remove the baking sheet from the oven.
Gently spread the tuna mixture evenly over the four slices of bread, making sure you get all the way to the edges. Sprinkle the Cheddar cheese evenly over the tops of the sandwiches.
Place the baking sheet with the sandwiches back into the broiler until the cheese is melted and bubbling, about 5-6 minutes.
