In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the diced onion and sauté for about 2-3 minutes until it becomes translucent.
Add the minced garlic and ginger to the skillet, stirring for about 30 seconds until fragrant.
Increase the heat to high and add the ground beef. Cook, breaking it apart with a spatula, until browned and cooked through, about 5-7 minutes.
Drain any excess fat from the skillet, then stir in the soy sauce, oyster sauce, sugar, and black pepper. Mix well to combine.
Add the sliced cabbage to the skillet, stirring to coat it with the sauce. Cook for an additional 4-5 minutes, or until the cabbage is tender but still slightly crisp.
Drizzle the sesame oil over the stir-fry and toss to combine. Remove from heat.
Serve hot, garnished with chopped green onions.