Place potatoes in saucepan; add 1/2 teaspoon salt and water to cover. Set aside for 1 hour.
Cook potatoes over medium heat for 30 minutes or until tender. Remove from pan; mash, and beat well with electric mixer until potatoes are smooth.
Combine butter, milk, remaining salt, and pepper; add to potatoes, stirring well. While mixture is warm, shape into 24 oval potato puffs, using about 1/4 cup of mixture for each puff. Place on a greased cookie sheet, and brush each potato puff with egg. Bake at 425° for 15 minutes or until lightly browned. Garnish with parsley.