In small bowl, combine reserved gravy, water, soy sauce, brown sugar, vinegar, sesame oil, garlic and ginger.
In large skillet over medium-high heat, heat 1 tablespoon oil. Add broccoli florets. Stir-fry 3 to 4 minutes, or until broccoli is bright green and crisp-tender. Add beef. Stir-fry 1 to 2 minutes. Add gravy mixture. Cook 2 to 3 minutes or until sauce, beef and broccoli are coated and warmed throughout.
Serve over rice. Sprinkle with sesame seeds.