Combine sauce ingredients in a medium bowl; set aside. Heat glaze ingredients in a small saucepan; keep warm.
Heat a wok or stir-fry pan over medium-high heat until hot. Add oil, swirling to coat sides. Add shrimp and remaining vegetables; toss and stir fry 2 – 3 minutes.
Add sauce; cook until lightly thickened.
To serve, place 2 heaping tablespoons of stir-fry mixture in center of an egg white omelet. Gather on top and carefully tie with a green onion strip. Continue making remaining purse omelets.
Serve in individual plates drizzle with warm glaze.