Preheat the oven broiler on high setting.
In a medium bowl, flake the drained tuna and combine with mayonnaise, Dijon mustard, celery, red onion, parsley, lemon juice, salt, and pepper.
Arrange bread slices on a baking sheet and toast under the broiler for 1 minute per side or until lightly golden.
Spread the tuna mixture evenly across the four toasted bread slices.
Place one slice of cheddar cheese on top of each sandwich.
Return the baking sheet to the broiler and cook for 2 to 3 minutes until the cheese is melted and bubbling.
Remove from oven and serve warm.