Blanch the carrots in a large pan of lightly salted boiling water for 10 minutes. Drain well and pat dry. Transfer to a bowl and spray with a little oil, then cook on a hot barbecue for 5—10 minutes, turning frequently, until charred.
Meanwhile, combine the dressing ingredients in a large bowl and season to taste. Stir in the cooked carrots, sunflower seeds and parsley and toss well. Serve hot.