Slice the beef against the grain into thin slices, about 1/4 inch thick. Place the slices in a bowl and add soy sauce, peanut oil, and cornstarch. Mix gently by hand until the beef is coated. Let it marinate for 10 minutes.

In a medium-sized bowl, mix all the sauce ingredients: chicken stock, Shaoxing wine, soy sauce, dark soy sauce, brown sugar, and cornstarch. Stir until well combined.

In a large nonstick skillet, add 1/4 cup of water over medium-high heat. Once the water boils, add the broccoli and cover. Steam the broccoli for about a minute until it's tender. Then, transfer it to a plate and wipe any excess water from the skillet.

Heat the peanut oil in the same skillet over medium-high heat. Spread the marinated beef in a single layer. Let it cook without moving for about 30 seconds until browned. Flip the beef and cook for a few more seconds until it's lightly charred but still pink inside.

Add minced garlic and ginger to the beef. Stir for a few seconds to release their flavors.

Return the steamed broccoli to the skillet. Stir the sauce mixture and pour it over the beef and broccoli. Cook and stir everything for about a minute until the sauce thickens. Transfer to a plate and serve hot.