Cut eggs in half the short way. Remove yolks and mash. Mix with milk, garlic, parsley, salt and pepper. Stuff whites, reserving two tablespoons of filling. Heat oil and butter. When it's foaming, place the eggs in the pan stuffed side down and fry on medium heat about two minutes. Put leftover filling, mustard, vinegar, water, salt and pepper in food processor. Slowly add 1/4 cup oil and process until oil is absorbed. Pour sauce in a gratin dish and arrange eggs on it yolk side up. Serve with French bread. (If you don't have a food processor, the sauce can be made with a wire whisk).