Heat vegetable oil in a large skillet or wok over medium-high heat. Add onion and cook for 3-4 minutes until softened.
Add garlic and ginger, cooking for 1 minute until fragrant.
Add shredded cabbage and carrots to the skillet. Cook for 8-10 minutes, stirring frequently, until cabbage is wilted and tender.
Stir in shredded chicken, soy sauce, and rice vinegar. Cook for 2-3 minutes until chicken is heated through.
Remove from heat and drizzle with sesame oil. Toss to combine.
Serve hot, garnished with sliced green onions and sesame seeds.