Place chicken in a shallow pot or non-stick pan with just enough water to keep it from burning. Season with salt and pepper. Cover, turn heat to medium and cook 5 minutes. Add peas to pan, cover and continue cooking 3 to 5 minutes more until chicken is tender and snap peas are blanched but still crunchy. Remove from heat, pour off liquid and let cool.
Place sesame tahini and sesame oil in a large salad bowl, whisk in lime juice and stir until combined. Add soy sauce, ginger, sugar and chili paste. Taste and adjust seasonings. Add chicken, snap peas, cabbage, peppers, sprouts, scallions, carrots and cilantro. Toss until all ingredients are coated with dressing. Serve immediately.