In wok or large, deep skillet, heat oil over medium-high heat. Add onion, garlic and ginger and stir-fry 3 minutes. Add cabbage and water. Cover and cook, stirring occasionally, until cabbage is tender, 5 minutes.
Add mixed vegetables and green onions and stir-fry just until tender, about 3 minutes. Stir in rice and sesame oil, then season to taste with soy sauce and pepper. Stir-fry 2 to 3 minutes, then serve.