Preheat the broiler and set the rack about 4 to 5 inches from the heat source.
Spread the bread out on a baking sheet and toast. Spread the toasted muffins or bread with the mayonnaise, if using. Top with the tuna salad and then the shredded cheese. Place the baking sheet under the broiler and heat for 3 to 5 minutes, until the cheese has melted. Serve immediately.