Cut eggs in half lengthwise, removing yolks. Reserve 4 egg yolks for another use. Chop whites and remaining 2 yolks. Combine egg, onion, and relish in a small bowl.
Combine mayonnaise, salt, curry, and pepper; add to egg mixture.
Place 1 lettuce leaf on the bottom half of each English muffin. Spoon one-third egg salad over leaves, and top with remaining muffin halves.