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In a medium bowl, mix drained tuna, mayonnaise, Dijon mustard, chopped celery, red onion, chopped dill pickles, and season with salt and pepper to taste.
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Spread a thin layer of softened butter on one side of each slice of bread.
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Lay out the bread slices on a baking sheet.
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Flip two of the bread slices over, so the buttered side is facing down.
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Evenly distribute the tuna mixture over the unbuttered side of the two slices.
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Top each with a slice of American or cheddar cheese.
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Place the remaining two slices of bread on top of the tuna and cheese slices, buttered side up.
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Broil on low until the cheese is melted and bubbly and the slices of bread are toasted. This can take about 2-3 minutes.
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Flip sandwich over half way through cooking.
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Remove from the oven and slice the sandwiches in half.