In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain excess fat if necessary.
Add the sliced onion, garlic, and ginger to the skillet. Stir-fry for about 2-3 minutes until the onion is translucent.
Add the sliced cabbage to the skillet and stir well to combine. Cook for another 5-7 minutes, stirring occasionally, until the cabbage is tender but still slightly crisp.
In a small bowl, mix together the soy sauce, oyster sauce, sesame oil, sugar, and black pepper. Pour this sauce over the beef and cabbage mixture, stirring to coat everything evenly. Cook for an additional 2 minutes to heat through.
Remove from heat and garnish with chopped green onions before serving.