In a large, non-reactive bowl, combine the cabbage, bell pepper, onion and carrot, season with the salt and pepper and cover with plastic wrap. Refrigerate for 1 hour before proceeding.
Meanwhile, combine the vinegar, sugar, mustard and celery seeds in a small saucepan and bring to a boil. Stir the vinegar periodically to dissolve the sugar. Once the sugar is dissolved, remove from the heat. Remove the cabbage from the refrigerator and pour the vinegar over the top of the cabbage. Add the oil, green onions and parsley, and toss well to thoroughly combine.
Cover with plastic wrap and return the cabbage to the refrigerator. Allow slaw to sit for 2 or 3 hours before serving, stirring occasionally. Serve with barbecue.