Mince shallot and combine with the remaining dressing ingredients. Set aside.
Season chicken with your favorite herbs and spices (some great flavors are turmeric and ginger).
Line baking dish with foil, add seasoned chicken, and bake for 20 minutes or until chicken is no longer pink inside. Allow to cool slightly, then chop or shred.
While chicken is cooking, chop celery, peel and chop carrots, slice onion into rings, dice cucumber, remove seeds from the pepper and cut into strips, and roughly chop lettuce and cabbage.
Toss all veggies into a large mixing bowl (including raw sugar snap peas), and season with salt and pepper; add chicken and dressing, then toss until everything is well coated.