For the Marinade and Shrimp:
For the Marinade
In a mixing bowl whisk together the egg white, soy sauce, dry sherry, and cornstarch.
Add the shrimp and toss to coat.
Cover with plastic wrap and set aside for 10 minutes.
For the General Tso's Sauce
In a separate medium mixing bowl combine the chili sauce, soy sauce, dry sherry, hoisin sauce, sesame oil, cornstarch, and water; whisk until incorporated. Set aside.
For the Stir Fry
Add half of the vegetable oil to a wok or large skillet and heat it over high-heat.
Remove shrimp from marinade; discard marinade.
In batches, cook the shrimp for about 1 minute per side, or until they turn pink.
Remove from skillet and set aside on a plate.
Add remaining oil to the skillet and heat it up.
Stir in broccoli florets and cook for 3 minutes.
Stir in green onions and continue to cook for 2 more minutes.
Stir in garlic; cook for 10 seconds.
Stir previously prepared General Tso's sauce and add it to the skillet; cook for a minute or two, or until thickened.
Add shrimp back to the skillet and stir around to coat in the sauce; cook for a minute or until heated through.
Remove skillet from heat.
Arrange shrimp and broccoli over cooked rice.
Garnish with red pepper flakes and sesame seeds.