Make the Tuna Salad Filling. Start by draining the canned tuna and placing it in a bowl. Flake the tuna with a fork. Add the mayonnaise, Dijon mustard, finely chopped celery, and red onion. Mix everything together until well combined. Taste and adjust with salt and pepper to your liking.
Prepare the Bread and Cheese. Spread butter on one side of each slice of bread. Lay the bread butter-side-down on a clean surface. Place a slice of your chosen cheese on each piece of bread. Spoon a generous amount of the tuna salad mixture on top of the cheese, ensuring an even spread. Top with another slice of cheese, then place the second piece of bread on top, butter-side-up.
Cook the Tuna Melt. Heat a non-stick skillet over medium heat. Once hot, place the assembled tuna melt sandwiches in the skillet. Cook for about 3-4 minutes on each side, or until the bread is golden brown and crispy, and the cheese is fully melted. Press down gently on the sandwiches with a spatula to help the cheese melt evenly.
Serve and Enjoy. Once both sides are crispy and the cheese is perfectly melted, remove the sandwiches from the skillet. Let them cool for a minute before cutting them in half. Serve immediately with a side of pickles, chips, or a light salad.