Place potatoes in a large saucepan and cover with water. Bring to a boil and add 1 teaspoon of the salt. Cook over medium heat 15 minutes or until tender. Drain and set aside to cool.
Cut eggs in half and place yolks in a large bowl; mash yolks with a fork and stir in oil and TABASCO® Green Sauce. Add mayonnaise and remaining 1 teaspoon salt and mix well. Dice potatoes and add to mayonnaise mixture along with celery, green pepper, and pickle relish. Finely chop egg whites and stir into salad, mixing well. Refrigerate until ready to serve.
Makes 8 servings.