In a mixing bowl, combine the drained tuna, mayonnaise, dill relish, finely chopped red onion, finely chopped cilantro, and lime juice.

Season the tuna mixture with freshly ground black pepper and kosher salt, to taste.

Stir until well combined.

Butter one side of each slice of sourdough bread.

Place one slice of bread, buttered side down, on a clean surface.

Layer half of the sliced Cheddar cheese on top of the bread.

Spoon the prepared tuna mixture evenly on top of the cheese.

Arrange the remaining slices of Cheddar cheese on top of the tuna.

Place the second slice of bread on top of the cheese, with the buttered side facing outwards to form a sandwich.

Preheat a skillet or griddle over medium heat.

Carefully transfer the sandwich to the skillet or griddle.

Cook the sandwich for about 4 minutes on each side, or until the bread is golden brown and the cheese is melted.

Once cooked, remove the sandwich from the skillet or griddle and let it cool slightly before serving.

Slice the sandwich diagonally and serve warm, accompanied by your favorite side salad or soup.