Prepare all your ingredients ahead of time by slicing the cabbage, bell pepper, and carrots, and mincing the garlic and ginger.
Heat the vegetable oil in a wok or large skillet over medium-high heat.
Add the minced garlic and grated ginger to the hot oil, stirring quickly to avoid burning, and sauté for about 30 seconds.
Add the sliced bell pepper and carrots to the wok, and stir-fry for 2-3 minutes until they begin to soften.
Toss in the sliced cabbage and snap peas (or green beans). Stir-fry for about 5-7 minutes, or until the cabbage is tender but still has a crunch.
Pour the soy sauce, rice vinegar, and sesame oil over the vegetables and mix well. Cook for an additional 2 minutes to heat through.
Season with salt and pepper to taste, adjusting according to your preference.
Remove from heat, and transfer the stir-fried cabbage to a serving bowl. Garnish with chopped green onions and sesame seeds, if desired.