Drain the 4 ounces albacore tuna well, pressing out any excess water, then place it in a bowl and mash or flake into small chunks.
Add ¼ cup mayonnaise, ¼ teaspoon Dijon mustard, ¼ cup chopped celery, 2 tablespoons pickle relish, 1 tablespoon chopped red onion, and the ? teaspoon kosher salt from the ingredients list. Mix until evenly combined.
Spread one side of each of the 4 slices of white bread with the 2 tablespoons butter.
Heat a large nonstick or cast-iron skillet over medium-low heat.
Place two buttered-side-down slices of bread in the skillet (or work one sandwich at a time if your skillet is small). On each buttered-side-down slice place one slice American cheese.
Divide the tuna mixture evenly onto the two slices with American cheese, then top each portion with one slice provolone.
Place the remaining two slices of bread on top with the buttered sides facing up (so the unbuttered sides touch the tuna and cheese). Gently press each sandwich with a spatula, cover the skillet with a lid, and cook 2–4 minutes until the bottom is golden brown.
Flip the sandwiches, cook another 2–4 minutes until the other side is golden brown and the cheeses are melted.
Remove from the skillet, let rest about 1 minute, slice, and serve.