Spread the lettuce out on a large serving dish or bowl. Sprinkle the onion, celery, water chestnuts and frozen peas (unthawed) over the lettuce in layers. Spread mayonnaise over the top like a frosting. Sprinkle with sugar and grated cheese. Cover and refrigerate overnight.
Place bacon in a large, deep skillet. Cook over medium-high heat until evenly brown. Drain, crumble and set aside.
Before serving, sprinkle crumbled bacon over the top, and garnish with tomato wedges, slices of hard-cooked egg, and parsley.