1. In a 4- to 5-quart pan over high heat, bring 2 quarts water, ginger, and salt to a simmer. Add chicken, adjust heat to maintain simmer, and cook until chicken is slightly pink in the center (cut to test) about 10 minutes. Remove from heat and let stand for 10 minutes, then lift chicken from water. When cool enough to handle, shred or slice into bite-size pieces.
2. In a large bowl, mix lemon juice, honey, fish sauce, soy sauce, garlic, vinegar, and chili paste. Add cabbage, carrots, jicama, cucumber, onion, celery, cilantro, mint, and chicken; mix well. Sprinkle with sesame seeds.