Wash and scrub potatoes with a soft vegetable brush. Cut into quarters. In a medium saucepan, cook potatoes, covered, in enough lightly salted boiling water to cover for 20 to 25 minutes or until tender. Drain. Mash with a potato masher or beat with an electric mixer on low speed. Let stand about 10 minutes or until cool enough to handle.
Meanwhile, in a medium skillet, cook onion, sweet pepper, Cajun seasoning, and salt in 2 teaspoons hot oil over medium heat until onion is tender. Add to potatoes along with parsley; mix well. Shape mixture into six 1/2-inch-thick patties. Place on baking sheet. If desired, cover and chill until ready to cook.
Place a very large skillet on grill side burner. In the skillet, heat 2 tablespoons oil over medium-high heat for 4 minutes. Add potato patties; reduce heat to medium. Cook for 6 to 8 minutes or until patties are golden brown, carefully turning once. If necessary, add additional oil during cooking. Remove patties from skillet. Serve immediately or cover and keep warm. Makes 6 patties.