1. Place the potatoes in boiling salted water to cover, and cook until theY'are tender but do not fall apart when gently pierced with a knife. Drain them in a colander and when they are cool enough to handle, peel and cut them into ½- to ¾-inch cubes.
2. Place the potatoes in a large bowl and gently stir in the salt, vinegar, celery, onion, green pepper and parsley.
3. To make the mayonnaise, beat the egg yolks with a whisk or rotary or electric beater for 2 to 3 minutes until they thicken and cling to the beater. Add the lemon juice, vinegar, mustard, salt and pepper.
4. Beat in the oil ½ teaspoon at a time until ¼ cup is used, making sure each spoonful is absorbed. Still beating, slowly add the rest of the oil. Gently fold the mayonnaise into the potatoes. Taste for seasoning. Garnish with egg slices and chopped parsley.