Prepare the Vegetables: Cut the cabbage into small, bite-sized chunks. Julienne the carrots if using, and chop the onion and green onions. Mince the garlic and beat the eggs in a small bowl.

Cook the Eggs: Heat 2 tablespoons of cooking oil in a large wok or skillet over medium heat. Add the beaten eggs and cook, stirring gently, until they are scrambled but still soft.

Sauté the Aromatics: In the same pan, heat an additional 2 tablespoons of oil. Add the garlic and onion, cooking for about 2 minutes until they become fragrant and translucent.

Sauté the Vegetables: Toss the cabbage and carrots (if using) into the pan. Stir-fry for 5-7 minutes until the vegetables are tender yet retain a bit of crispness.

Add the Sauces: Pour in the soy sauce, oyster sauce, sesame oil (if using), salt, and sugar (if using). Stir well to coat the vegetables evenly in the savory sauce.

Combine Everything: Return the scrambled eggs to the pan along with the green onions. Toss everything together and cook for 1-2 minutes until well combined and heated through.

Plate and Serve: Spoon the stir-fry into a serving dish and serve immediately. For a well-rounded meal, pair it with steamed rice or noodles.