A note about beef. Just about any cut will do, so don't feel you need to buy "the best". Make sure you cut your beef against the grain. This means when you look at your slice it will look like you cut through a handful of straws where all you see is little circles. If you cut your beef "with" the grain you will have chewy strips. Not good!
Cut beef into 1/4 inch thick strips.
In a medium bowl mix together the beef strips and tamari sauce. Stir well making sure every piece is coated.
To the beef mixture add the white sugar and black pepper, stirring for 3 minutes to combine and help the sugar dissolve.
Add the whipped egg white and cornstarch, again stirring for 3 minutes. You DO NOT want to see any sugar or cornstarch.
Cover and let stand in the fridge for 3 hours, stirring once at 1 and 1/2 hours.
Bring wok or very large skillet to medium-high heat.
Add the vegetable oil and sesame oil.
Stir-fry the broccoli for 4 minutes, stirring constantly. Using a slotted spoon remove to a bowl and set aside.
Add minced garlic to wok giving it a quick stir. Do not let it brown.
Add meat to the wok and stir-fry until "just" done, around 4-5 minutes tops.
Return broccoli to wok, give it a good stir.
Add the sherry and oyster sauce, stirring/tossing for 1 minute to make sure beef and broccoli is well coated with sauce.