Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced onion and sauté for about 2 minutes until it starts to soften.
Stir in the minced garlic and grated ginger, cooking for an additional 30 seconds until fragrant.
Add the julienned carrot and sliced red bell pepper, cooking for another 2-3 minutes until they begin to soften.
Toss in the shredded cabbage and stir well to combine all the vegetables. Cook for 5-7 minutes, stirring frequently, until the cabbage is tender but still crisp.
Pour in the soy sauce, rice vinegar, and sesame oil. Stir to coat the vegetables evenly. Season with salt and pepper to taste.
Remove from heat and garnish with chopped green onions and sesame seeds before serving.