Bring chicken broth to a boil in a saucepan then add rinsed quinoa. Place a lid on top then lower heat and cook until quinoa has absorbed chicken broth, about 15 minutes. Fluff with a fork then set aside. (Can be done ahead of time.)
Combine all sauce ingredients in a microwave-safe bowl then microwave for 20 seconds. Stir until smooth then set aside. Whisk together egg and sesame oil in a small bowl and set aside.
Heat 1 teaspoon peanut oil in a wok or large skillet over high heat. Season chicken with salt and pepper then add to wok and stir fry until no longer pink. Remove to a plate and set aside.
Heat remaining teaspoon peanut oil in wok, adding coleslaw mix, frozen edamame and green onions. Stir-fry until tender, 2 to 3 minutes, then push to outsides of wok, creating a clear space in the center. Add egg whisked with sesame oil to center of wok then stir fry until soft scrambled.
Add cooked chicken, quinoa, sauce and half the chopped peanuts to wok and toss to combine. Serve with remaining chopped peanuts.