In a small bowl, add broth, soy sauce, brown sugar, garlic, ginger, cornstarch and red pepper and whisk until combined. Slice beef against the grain into thin slices then place in a medium-sized bowl. Pour ¼ cup sauce over beef and stir to coat. Set aside for 15–20 minutes to let beef marinate.
Place a wok or large skillet over medium-high heat and allow it to become hot. Add broccoli and water then cover, stirring frequently, until the florets become bright green and are cooked through but not mushy—about 5–6 minutes. It may be necessary to add a bit more water if it gets too dry but all water should be evaporated by the time broccoli is tender. Transfer broccoli to a plate then cover loosely to keep warm and set aside.
Return skillet or wok to heat then add oil. Allow oil to get hot, then add beef. Stir-fry the beef for about 3–4 minutes until it is no longer pink. Pour in reserved sauce and cook, stirring constantly, until sauce comes to a boil.
Reduce heat and simmer for about 1 minute until sauce is very thick and glossy. Add broccoli and stir to coat with sauce. Continue cooking only until broccoli is heated through and has reached desired tenderness. Remove from heat and serve immediately.
Notes
Place meat in the freezer for 15 minutes prior to slicing—it will firm up and become much easier to cut thin slices!