In large bowl mash black-eyed peas with a potato masher. Add egg, sweet pepper, bread crumbs, celery, green onions, and garlic salt; mix well. Shape bean mixture into twelve 1/2"-inch thick patties about 3"-inches in diameter.
In large skillet heat 1 tablespoons of the oil over medium heat. Add half of the patties to the hot oil. Cook 8 minutes or until lightly browned and heated through, turning once. Remove and keep warm. Repeat with remaining oil and patties.
In small bowl stir together mayonnaise and Cajun seasoning. Spread cut side of each roll with the mayonnaise mixture. Place a burger on bottom half of each roll; top with lettuce and add roll top.