Rinse cauliflower under running water and remove green leafs. Cut into quarters. Steam cauliflower until tender, about 12-15 minutes. Drain and cool, then cut into bite-size pieces.
Meanwhile, bring six eggs to a boil, boil for 12 minutes. Drain and cool. Crack and peel eggs. Separate whites from yolks. In a small bowl, mash the yolks with a fork. Cut whites into bite-size pieces. (Reserve 2 eggs for garnish)
Dressing: In a small bowl, combine mayonnaise, mustard, sweet relish, onion, and celery.
In a large bowl, gently toss cauliflower, egg whites, egg yolks, and dressing together. Season with salt and pepper. Garnish with reserved eggs and parsley if desired. Chill at least 2 hours before serving.