After draining the tuna thoroughly, place it into a medium bowl. Use a fork to break it up really well.
Mix mayonnaise, onion, lemon juice, salt, pepper, celery and green onion with the tuna.
Heat a skillet to medium-low heat. Spread butter on one slice of bread.
Place this piece of bread, butter side down, into the skillet. Add about ½ cup of the tuna mixture and spread it to the edges of the bread.
Add slices of tomato and a slice of cheese.
Butter on one side of another piece of bread. Place this piece of bread (butter side up) on top of the cheese. (The butter goes on the outside of the sandwich so that it will toast nicely.) Then carefully flip the sandwich with a spatula to grill both sides.
Cook the sandwich in the skillet at medium-low heat until the cheese is melted and the bread is toasted.
You can use a variety of breads for this recipe, see my ideas above.
If you are not a fan of cheddar cheese, feel free to swap it out, there are more ideas above.
The tuna salad itself can be frozen for up to 1 week.