To prepare marinade, combine first 5 ingredients in a medium bowl; cover and chill 20 minutes.
Heat 1 tablespoon of the vegetable oil in a wok or large nonstick skillet over medium-high heat. Add the chicken mixture; stir-fry 4 minutes or until chicken is done. Remove from pan; set aside.
To prepare sauce, combine broth and next 6 ingredients (broth through 1 teaspoon sesame oil); stir well with a whisk. Heat 1 tablespoon vegetable oil in pan. Add 2 tablespoons green onions, ginger, garlic, and chile paste, and stir-fry for 15 seconds. Add broth mixture, and cook 1 minute or until thick, stirring constantly.
Stir in cooked chicken, water chestnuts, sliced onion tops, and peanuts; cook for 1 minute or until thoroughly heated. Serve over rice.