In a large skillet or wok, heat the sesame 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. Sauté for about 3-4 minutes until the onion is translucent.
Stir in the shredded cabbage and cook for another 5 minutes, stirring frequently, until the cabbage is wilted.
In a small bowl, mix together the soy sauce, rice vinegar, brown sugar, and black pepper. Pour this mixture over the beef and cabbage, stirring well to combine. Cook for an additional 2-3 minutes to heat through.
Remove from heat and garnish with sliced green onions before serving.