Begin by thinly slicing the beef, then marinate it in a bowl with cornstarch, Shaoxing wine, salt, and black pepper for 15 minutes. Meanwhile, chop the ripe tomatoes into wedges.

In a non-stick skillet, heat half a tablespoon of vegetable oil over medium heat. Pour in the lightly beaten eggs and cook gently, stirring constantly until they are just set and fluffy, about 2-3 minutes. Once done, transfer the scrambled eggs to a plate and set aside.

In a wok, heat one tablespoon of vegetable oil over high heat until shimmering. Add the marinated beef strips, quickly stir-frying for about 3-4 minutes until browned and cooked through. Remove the beef from the wok and keep it warm.

In the same wok, add another tablespoon of oil if needed. Reduce the heat to medium and stir-fry the white parts of the green onions for 1-2 minutes until fragrant.

Add the chopped tomato wedges into the wok, along with ketchup, brown sugar, and beef broth. Increase the heat and bring to a boil, then reduce to a simmer. Mix in the cornstarch slurry and stir for about 5 minutes until the sauce thickens.

Return the cooked beef and scrambled eggs back into the wok with the sauce. Gently toss everything together for a minute, ensuring the beef and eggs are well coated.

Transfer the mixture onto plates. Garnish with the green tops of the green onions. Serve hot over a bed of steaming white rice.