In a large skillet (one with a lid), heat the walnut oil over medium heat. Stir in the ginger and garlic and keep stirring. When oil starts sizzling, add the leek and chili pepper and sauté until leek is softened.
Stir in the shredded cabbage, cover skillet and cook around 6 minutes or until cabbage is softened but still a bit crisp, stirring halfway through. Season to taste with salt and pepper.