Cook potatoes in boiling water to cover 40 minutes or until tender; drain and cool. Peel and cut into 1-inch cubes.
Chop egg whites. Stir together potato cubes, egg whites, 1/2 teaspoon salt, and, if desired, green onions.
Mash egg yolks; add remaining 1/2 teaspoon salt, mayonnaise, and next 3 ingredients, stirring until blended. Gently stir into potato mixture. Cover and chill 2 hours.