Cut out the firm core of each half of cabbage and discard. Cut each half and half lengthwise, then cut everything crosswise into very thin strips. Toss the cabbage together in a large bowl.
Peel the carrots, then use a vegetable peeler to cut the carrots, then use a vegetable peeler to cut the carrots into long strips (not including the light cores). Roughly chop the carrot strips into pieces about 1 inch long. Add them to the bowl.
Combine the parsley, vinegar, olive oil, and Worcestershire sauce in a jar and season it with the salt and pepper to taste. Shake the dressing well, adjust the seasoning to your taste, drizzle it ovver the cabbage and carrots. Toss the slaw to coat it. Refrigerate for at least 1 hour or overnight, before using.
