In a 2-quart pot, place the eggs. Cover with water by 2 inches and salt the water liberally. Bring the water to a boil and then cover, turn off the heat, and let sit for 8 minutes.
Grate the hard boiled eggs on a cheese grater. In a small bowl, combine the eggs, mayonnaise, and cheese. Adjust the seasoning of the egg mixture with hot sauce, salt, and pepper, to taste. Layer bread with egg mixture and serve as double decker sandwiches.