Make the tuna salad. In a medium bowl, combine the drained tuna, mayonnaise, Dijon mustard, diced celery, red onion, lemon juice, salt, and pepper. Use a fork to flake and mix everything together until well combined but not pasty. Taste and adjust seasoning with more salt, pepper, or lemon juice. Set aside.
Butter the bread. Lay out your four slices of bread. Using softened butter, generously spread it on one side of each slice. This buttered side will go face-down in the pan, creating that essential golden, crispy crust. Trust me, don't skimp here—it's the key to texture.
Assemble the sandwiches. Place two slices of bread, buttered-side down, on your work surface. Divide the tuna salad evenly between them, spreading it to the edges. If using, add two slices of tomato per sandwich (pat them dry first to prevent sogginess). Top each with a generous layer of sharp cheddar cheese. Cap with the remaining bread slices, buttered-side facing out.
Cook to golden perfection. Heat a large skillet or griddle over medium-low heat. Carefully place the assembled sandwiches in the pan. Cook for 4-5 minutes, until the bottom is deeply golden brown and crisp. Tip from me: Resist the urge to press down with a spatula—you'll squeeze out the filling. Just let it be.
Flip and finish cooking. Using a wide spatula, carefully flip each sandwich. Continue cooking for another 3-4 minutes, until the second side is golden brown and the cheese is fully melted. If the bread is browning too quickly before the cheese melts, reduce the heat slightly and cover the pan for a minute to trap heat.
Rest and serve. Transfer the cooked tuna melts to a cutting board and let them rest for 1-2 minutes. This allows the filling to set slightly, making them easier to cut. Slice in half diagonally and serve immediately with pickle spears, potato chips, or a simple side salad.