Combine potatoes, onion, 1/2 teaspoon of the salt and water to cover and boil until potatoes are soft.
Drain, reserving liquid, and force potatoes through food mill or sieve.
Blend together garlic, remaining salt and egg yolks; gradually add oil, stirring constantly.
Combine with sieved potato and reserve 3/4 cup.
Add remaining garlic-potato mixture to reserved potato water and blend well.
Adjust seasonings with salt and pepper.
Mix reserved potato-garlic mixture with flour, adding more flour if needed to form a mixture that can be shaped into balls.
Form marble-sized balls, return soup to boil, add balls, lower heat slightly and cook 5 minutes.
Garnish with parsley.