Spread lettuce out on a large serving dish or bowl. Sprinkle onion, celery, water chestnuts, and frozen peas (unthawed) over lettuce in layers. Spread mayonnaise over 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 top, and garnish with tomato wedges, slices of hard-boiled egg, and parsley.
