In a bowl, combine the tuna, mayonnaise onion, relish, mustard, 1/2 teaspoon salt, and 1/4 teaspoon pepper and mix until incorporated.
Spread one tablespoon of butter on one side of each piece of bread, then flip the slices over so they are buttered-side down. Divide the tuna mixture between two slices of bread, then top with the tomato slices and cheddar. Place the remaining two slices of bread on top, buttered-side up.
Heat a heavy cast iron pan over low heat and toast the sandwiches in it until the cheese is melted and the bread is golden and toasty, five to six minutes per side.
