Quarter and core the cabbage. Peel the carrots and onion and cut into pieces that will fit through the feed tube of a food processor. Fit the food processor with the grater attachment and push the cabbage, carrots and onion through the feed tube to grate. Toss the grated vegetables in a large bowl.
Prepare the coleslaw dressing by whisking together the mayonnaise, mustard, cider vinegar, sugar, 1 teaspoon black pepper and the cayenne in a medium bowl. Toss the dressing with the cabbage mixture and season with salt and pepper. Cover with plastic wrap and chill at least 2 hours before serving.