Place the 1-inch piece of ginger and star anise in a pot of water over medium-heat and bring to a boil. Add chicken to the water. Lower heat to medium-low; simmer until chicken is no longer pink the middle, 10 to 12 minutes. Remove to a plate to cool. Once cool to the touch, dice into bite-sized pieces.
Make a dressing by whisking together the mayonnaise, salt, pepper, paprika, and honey; set aside.
Combine the diced chicken, celery, apple, onion, raisins, walnuts and 2 teaspoons minced ginger in a bowl. Drizzle dressing into the chicken mixture; stir until pieces are evenly coated. Cover and refrigerate overnight.