Chop 2 lettuce leaves. Cut 4 thin slices from part of tomato; chop remaining tomato.
Combine chopped lettuce, chopped tomatoes, egg, cheese, bacon and dressing. Remove bread from inside centers of tops of rolls, leaving 1/2-inch-thick shells; discard removed bread or reserve for another use.
Spread mayonnaise onto bottom halves of rolls; top with lettuce leaves, tomato slices, ham and chopped salad. Cover with tops of rolls.