Heat olive oil in a large skillet over medium-high heat.
Add ground beef and cook until browned, breaking it apart. Season with salt and pepper.
Add diced onion and carrot. Cook for 5–7 minutes until onion is translucent and carrot is tender.
Stir in garlic and cook for 30 seconds.
Add cabbage, ground ginger, soy sauce, sesame oil, and sugar. Stir well.
Cook for another 5–7 minutes until cabbage is tender.
Garnish with green onions and sesame seeds if desired. Serve warm.