Marinate the beef — Combine soy sauce, brown sugar, sesame oil, garlic, ginger, and grated pear in a bowl. Add the sliced beef and onion, toss to coat, and marinate for at least 30 minutes (or overnight for deeper flavour).
Cook the bulgogi — Heat vegetable oil in a large pan or skillet over high heat. Add the marinated beef in batches, cooking 2–3 minutes per side until caramelised and cooked through. Don't overcrowd the pan.
Assemble the bowls — Divide steamed rice between two bowls. Arrange the bulgogi, kimchi, carrot, and cucumber over the rice in sections.
Finish and serve — Top with a fried egg if using, scatter with green onions and sesame seeds, and serve hot.