Place the shredded cabbage and shredded carrot (optional) into a small mixing bowl (medium bowl if doubling the recipe). Stir in the vegan mayonnaise and vinegar. Add sugar (optional), salt and black pepper, to taste. Place in the refrigerator to chill.
To make the chili sauce:
In a dutch oven or soup pot, combine the yellow onion, tomato sauce, tomato paste, chili powder, salt, black pepper and garlic powder. Add one cup of water. Mix well.
Bring the chili sauce to a boil, reduce heat, and simmer for 40 minutes. Add the vinegar and simmer 30 minutes longer, until the sauce is as thick as a paste and doesn’t cover the pan bottom after parting it with a spoon. Remove from heat.
In the meantime, while the chili sauce is cooking, brown the vegan ground (do not season it) and cook 4 to 6 vegan weiners. Set aside. When the sauce is nearly done cooking, toast the hotdog buns.
Stir the vegan ground into the cooked chili sauce mixture to coat.
To assemble the hot dogs:
Place a cooked weiner and mustard on each of the toasted buns. Top with a generous amount of the chili sauce. Add coleslaw on top of the chili sauce, then sprinkle with some of the chopped onion. Serve immediately.
The chili sauce and slaw will keep in the refrigerator for 2 to 3 days. For serving, they can be made a day ahead, and the sauce can be reheated in a saucepan. The chili sauce can be kept in the freezer for up to two months.