Combine all ingredients except lettuce and green onions in a bowl. Cover, Refrigerate 8 hours or overnight; stir occasionally. Drain, reserve marinade.
Broil shrimp 4 inches from heat until cooked and tender. (about 2 minutes on each side, less for small shrimp) Do not overcook or shrimp will become tough. Brush occasionally with marinade.
Serve shrimp on shredded lettuce; sprinkle with chopped green onion. (marinade may be heated and served for dipping, if desired) Makes 6 servings