Yolk mixture:
Cut eggs in half and remove yolks.
Mix yolks with garlic, parsley, salt, pepper, and milk.

Make the eggs:
Stuff eggs with mixture, reserving 2 tablespoons for the sauce.
Sauté the eggs in olive oil, cut side down for maybe two minutes.

dressing (sauce):
While doing that, mix remaining egg mixture with mustard, red wine vinegar, and water to make a sauce.
Add olive oil until mixed.

Place sauce mixture on serving platter and add the eggs to the top.