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