Press breasts with hands to make of uniform thickness. Cut in 1-½-inch squares. Mix cornstarch, ½ teaspoon (or less) salt, pepper, sugar, 1 tablespoon soy sauce, and 2 tablespoons oil. Add chicken and stir to coat evenly. Saute walnuts until golden in 1 tablespoon oil. Sprinkle with salt (optional). Heat remaining oil, add chicken mixture and stir-fry for 2 minutes. Add ham and walnuts and stir-fry for about 5 minutes. Stir in remaining soy sauce and broth, scraping up brown bits from bottom of pan. Cook for 1 minute longer. Serve with white rice.