Place cornstarch in a large bowl; gradually whisk in water until smooth. Then, whisk the eggs into cornstarch mixture. Once eggs are mixed, toss steak in mixture to coat.
Whisk sugar, rice vinegar, soy sauce, sesame oil, and red pepper together in a small bowl. Pour sauce mixture over vegetables in wok and bring mixture to a boil. Stir beef back into vegetable mixture; cook and stir just until heated through, about 3 minutes.
Serve alone or over rice, which can also be cooked in the wok! Enjoy!