In a large mixing bowl, combine the drained tuna, finely diced celery, minced red onion, and parsley. Mix them until evenly distributed.
Slowly add mayonnaise to the mixture, stirring as you go. The goal is to create a creamy mix without overpowering the tuna.
Stir in the mustard, lemon juice, and season with salt and pepper to taste. Give the mixture a good stir to ensure all ingredients are well-blended.
Take a slice of bread and spread a generous portion of the tuna salad mixture on top. Place a slice of cheese over the tuna mixture, followed by another slice of bread.
In a skillet or on a griddle, heat a small amount of butter over medium heat. Once melted, place the sandwich in the skillet. Cook until the bread is golden brown, then flip and toast the other side until the cheese melts and the bread is crispy.
Once toasted, remove the sandwich from the skillet, and layer tomato slices on top if desired. You can also add an extra slice of cheese before closing the sandwich for an even cheesier experience.
Slice the tuna melt in half, serve hot, and enjoy the melty, delicious goodness!