Heat vegetable oil in a large skillet over medium-high heat.
Add garlic and ginger; sauté for about 30 seconds until fragrant.
Introduce the chopped cabbage and carrots to the skillet.
Stir-fry for 3-5 minutes until the cabbage is slightly wilted.
Pour in the soy sauce and sesame oil, mixing well.
Add green onions, continuing to stir-fry for another 2 minutes.
Season with salt and pepper to taste.
Cook until vegetables are tender but still crisp.
Remove from heat and let it cool slightly.
Serve hot, garnished with sesame seeds.