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In a medium mixing bowl, combine beef with pepper, soy sauce, cooking wine, cornstarch and oil until evenly coated. Set the beef aside, allowing it to marinate for at least 10 minutes.
Heat oil in a large skillet over medium-high heat for 2 minutes until the hot oil sizzles. Add in the marinated beef and stir fry until nicely browned on all sides, about 3-4 minutes. Add garlic and ginger. Sauté together until fragrant, about 1 minute. Transfer the beef mixture to a plate.
In another bowl, whisk together all the sauce ingredients until the sugar and cornstarch is fully dissolved. Set aside.
In the same skillet over medium-high heat, add the remaining 1 tablespoon oil, broccoli and the sauce mixture. Cover the lid and let the broccoli simmer in the sauce until tender, about 2-3 minutes, stirring occasionally. The broccoli should be crunchy tender but still green.
Return the beef to the skillet and stir well to combine. Cook for another minute until evenly coated with thickened sauce.
Sprinkle sesame seeds on top and serve immediately with steamed rice.