Trim broccoli florets so stems are 1 to 1 1/2-inches in length. (Tip: Cutting stems on the diagonal gives the broccoli a more aesthetic look.) Cut florets as needed to create bite-size pieces. Set aside.
Trim off any excess fat from the beef. Slice beef with the grain into 1 1/2-inch-wide pieces, then thinly slice those beef pieces against the grain diagonally (this makes the slices of beef more tender). Place beef slices in a medium mixing bowl with soy sauce and garlic. Stir to combine. Set aside and allow to marinade for 15 minutes.
While beef is marinating, prepare Stir-Fry Sauce: In a small mixing bowl, whisk together cornstarch, ground ginger, cayenne pepper, dry sherry and beef broth. Set aside.
Heat a wok or large skillet over high heat. When wok or skillet is hot, add 2 tablespoons of the oil. Allow oil to heat for about 30 seconds, then add the beef and stir fry until meat is browned (about 2-3 minutes). Remove beef from skillet and set aside in a bowl.
Add remaining 2 tablespoons oil to wok or skillet. Allow oil to heat about 30 seconds, then add broccoli and stir-fry for about 1 minute. Add 2 tablespoons water. Cover and cook for about 3 more minutes until broccoli is tender-crisp (taste one small piece of broccoli to test doneness). Add beef back to skillet along with Stir-Fry Sauce and stir until well blended and thickened (about 1-2 minutes).