Preheat oven to 325 degree F. In a large skillet melt margarine or butter over medium heat. Add carrots, parsnip, celery, and onion. Cook, covered, for 15 to 20 minutes or until tender and lightly golden, stirring occasionally. Stir in salt and pepper.
In a large bowl combine bread cubes and parsley; add carrot mixture. In a small bowl combine 1/2 cup chicken broth and egg. Drizzle bread mixture with the broth mixture, tossing lightly. Drizzle with additional broth, if necessary, to desired moistness.
Transfer stuffing to a 2-quart casserole. Bake, covered, for 35 to 40 minutes or until heated through. (Internal temperature should register 165 degree F with an instant-read thermometer.) Makes 8 to 10 servings.