This is coleslaw as made in the Piedmont area of North Carolina for barbeques, where it is referred to variously as BBQ slaw, Red Slaw, Red Coleslaw, Barbecued Coleslaw, etc. The ketchup gives the salad a dusty pink hue. This recipe feeds a crowd. Cut it in half if needed.
Meanwhile, mix together all the ingredients except the cabbage to make the dressing; put in fridge.
Core cabbage, remove outer leaves and discard; cut cabbage in half; grate cabbage.
In a large bowl, mix the cabbage with the dressing. Return to the fridge, covered, to chill at least an hour before serving.
Traditionally, the cabbage is grated into teeny chunks, as opposed to slices. Sliced is fine, though if your grater is fighting you, or you just don't have that extra time.If you're pressed for time, you can use a large bag of sliced cabbage coleslaw mix from the store instead of starting from a whole cabbage (in which case, also don't worry if it's sliced instead of coarsely ground bits.) If you're using a bag mix, probably just half the dressing recipe will do it.