Place rice and 2-1/2 cups water in a 2-3 quart pan; bring to boil over high heat. Reduce heat and simmer, covered, until liquid is absorbed, about 20 minutes.
Meanwhile, stir broth, cornstarch, lemon juice, soy sauce, honey, and ginger until smooth; set aside.
Cut chicken crosswise into 1/2 inch wide strips. Place wok or stir fry pan over high heat. When hot, add oil, then chicken. Stir often until chicken is no longer pink in center, 2-3 minutes. Lift out and cover to keep warm. To wok, add bell pepper, bok choy, and 2 tablespoons water. Cover tightly and cook until bell pepper is barely tender-crisp to bite, 1 1/2-2 minutes; lift out and set aside.
Stir broth mix, then pour into wok and stir, bubbling, about 1 minute. Gently mix in chicken and vegetables. Spoon rice into center of a platter and arrange chicken mix alongside, placing bok choy around rim of platter. Add additional soy sauce to taste.