Place squash cut side down in a microwave-safe dish. Microwave, uncovered, on high for 10-12 minutes or until tender.
Meanwhile, in a small bowl, combine the broth, soy sauce, sugar, cornstarch, vinegar and pepper flakes until smooth; set aside.
In a shallow bowl, whisk egg and soy sauce. Place cornstarch in another shallow bowl. Dip chicken in egg mixture, then coat with cornstarch. In a large skillet or wok, stir-fry chicken in oil in batches until no longer pink. Remove and keep warm.
Stir-fry broccoli and onion for 2-3 minutes or until crisp-tender. Stir cornstarch mixture and add to the pan. Bring to a boil; cook and stir for 1-2 minutes or until thickened. Add chicken; heat through.
When squash is cool enough to handle, use a fork to separate strands. Serve with stir-fry.