Optional Step: Heat a small pan to medium-high heat and add a thin layer of oil to it. Slice a few vegan wonton wrappers into strips. Fry them for 30 seconds each side until they are golden and crispy.
Mix the chili sauce and vegan mayo in a small bowl until they are fully combined. Place this in the refrigerator for now.
Bring a large pan or wok to medium-high heat and add the oil to it. Sauté the onions and mushrooms for about 5 minutes or until they are softened.
Stir in the soy sauce, garlic, ginger, white pepper, and apple cider vinegar.
Add half of the cabbage and carrots to the pan. Sauté this for about 3 minutes, stirring constantly. Add the rest of the cabbage and carrots when the first batch cooks down. Sauté this for another 3 minutes. Keep stirring and scraping the bottom of the pan as it cooks. The vegetables should be slightly softened but still have some crunch.
Remove the pan from the heat and then stir in the sesame oil. Serve the egg roll filling in a bowl by itself or over rice. Drizzle the spicy mayo on top and top the meal with sesame seeds, sliced green onions, and fried wonton strips.