Prepare the Beef and Sauce: In a bowl, toss the sliced beef with 1 tablespoon of cornstarch to coat. In another small bowl, mix the remaining 2 tablespoons of cornstarch, beef broth, soy sauce, and sugar, stirring until smooth. Set aside.
Sauté the Beef: In a spacious skillet or wok, warm 1 tablespoon of vegetable oil over medium-high heat until shimmering. Add half of the beef and stir-fry for 2-3 minutes, or until browned and cooked through. Transfer to a plate and repeat with the remaining beef, adding more oil if necessary.
Sauté the Vegetables: In the same skillet, add the remaining tablespoon of oil and heat over medium. Add shiitake mushrooms, bok choy, red peppers, celery, and green onions. Cook the mixture for approximately 5 minutes, stirring frequently, until the vegetables are tender yet retain a delightful crunch.
Combine and Thicken: Return the beef to the skillet with the vegetables. Pour the sauce over the mixture and stir to coat. Let it cook for another 2-3 minutes, allowing the sauce to thicken and evenly coat all ingredients.
Serve: Spoon the beef and vegetable stir-fry over a bed of hot, steamed rice. Top with additional green onions for an extra pop of flavor, if you like.