Set oven control to broil.
In medium bowl, mix tuna, mayonnaise, celery, onion, parsley, vinegar, salt and pepper.
Place bread slices on baking sheet. Broil with top about 4 to 6 inches from heat 1 minute or until lightly toasted.
Turn bread over on baking sheet. Spread untoasted side of each slice of bread with about 1/3 cup of the tuna salad, 1 slice of the cheese, 2 slices tomato and 1 of the remaining slice cheese. Return sandwiches to oven; broil 3 to 5 minutes or until cheese is melted.