Place egg in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool, peel and chop. Preheat oven to 300 degrees F (150 degrees C).
In a mixing bowl, combine the American cheese, mayonnaise, chopped egg and tuna. Then mix in the green pepper, onion, chopped sweet pickles, and the chopped olives. Mix thoroughly.
Butter the hamburger buns with about a 1/2 tablespoon for each. Fill the buns with the mixture and wrap in tinfoil.
Bake in preheated oven for 30 minutes, or until cheese is melted.
