Heat the oil in a large skillet over medium-high heat. Add ground beef and cook for 5 minutes, breaking it apart with a wooden spoon until no pink remains. Season with salt and pepper, then push beef to one side.
Add the diced onion and grated carrot to the empty side of the skillet. Cook for 4 minutes, stirring occasionally until softened.
Stir in the garlic and ginger. Cook for 30 seconds until fragrant, then mix everything together.
Add the sliced cabbage and stir well. Cook for 5 to 7 minutes, stirring occasionally, until cabbage is tender but still slightly crisp.
Pour in the soy sauce, sesame oil, and sugar. Toss everything to coat evenly and cook for 2 more minutes. Taste and adjust seasoning as needed.
Remove from heat and garnish with sliced green onions and sesame seeds. Serve warm.
