In a small bowl; combine tuna, mayonnaise, and diced onion. Gently fold in cheddar cheese until combined.
Butter one side of each slice of bread.
Heat skillet over medium heat. To make sandwich; take one slice of bread and place butter side down on skillet. Add 1/4 of the tuna mixture. Spread over slice of bread. Top with second slice of bread with butter side face up. Once bottom of bread has browned (about 2 minutes), flip and brown the second side.
Repeat with remaining ingredients. Serve warm with a side of chips and a pickle.