Slice flank or skirt steak against the grain into ¼ inch thick pieces. Combine beef with soy sauce, peanut oil, and cornstarch in a bowl; mix well. Let marinate for 10 minutes.

In a separate bowl, whisk together chicken stock, Shaoxing wine, soy sauce, dark soy sauce, brown sugar, and 1 teaspoon of cornstarch. Set aside.

Bring an inch of water to boil in a large skillet. Place broccoli in a steaming basket and steam for 1 minute until bright green; remove and set aside.

Heat 1 tablespoon of peanut oil in the skillet over high heat. Add marinated beef in a single layer, cooking for 30 seconds on each side until browned. Add garlic and ginger; cook until fragrant.

Return steamed broccoli to the skillet with beef. Pour the prepared sauce over everything and stir well. Cook on medium-high heat until the sauce thickens, about 1 minute.

Transfer Chinese Beef and Broccoli to a serving plate. Serve hot over fluffy rice.