Prepare the Beef: Heat 1 tablespoon of vegetable or sesame oil in a large pan or wok over medium-high heat. Add the thinly sliced beef strips and stir-fry for 3-4 minutes until browned and just cooked through.

Cook the Vegetables: In the same pan, add the remaining tablespoon of oil Incorporate the minced garlic and freshly grated ginger, stirring for approximately 30 seconds until they release their aromatic fragrance. Then, toss in the broccoli florets and carrot slices. Stir-fry for 4-5 minutes until the vegetables are crisp-tender.

Make the Sauce: In a small bowl, mix together the soy sauce, oyster sauce (if using), brown sugar, and beef broth (or water). Add the dissolved cornstarch mixture to the sauce to thicken it.

Combine Everything: Return the cooked beef to the pan with the vegetables. Pour the sauce over the beef and vegetables, stirring everything together. Continue cooking for an additional 2 to 3 minutes, allowing the sauce to thicken and evenly coat the stir-fried ingredients.

Serve: Transfer the stir-fry to plates or a serving dish. Top with sesame seeds and freshly chopped green onions, if you wish. Serve hot with rice or noodles for a complete meal.