To make the Eggs: Put the eggs in a small saucepan, and cover with boiling water. Bring to a very gentle boil, and let boil for 9 to 10 minutes. Drain off the water, and shake the eggs in a saucepan to crack the shells. (This will help in their removal later on.) Fill the saucepan with cold water and ice, and let the eggs cool for 15 minutes.
Shell the eggs under cold running water, and split them lengthwise. Remove the yolks carefully, put them in a bowl, and add the garlic, parsley, milk, salt, and pepper. Crush with a fork to create a coarse paste. Spoon the mixture back into the hollows of the egg whites, reserving 2 to 3 teaspoons of the filling to use in the dressing.
Heat the vegetable oil in a nonstick skillet, and place the eggs, stuffed side down, in the skillet. Cook over medium heat for 2 to 3 minutes, until the eggs are beautifully browned on the stuffed side. Remove and arrange, stuffed side up, on a platter.
To make the Dressing: Mix all of the dressing ingredients in a small bowl with a whisk or a spoon until well combined. Coat the warm eggs with the dressing, and serve lukewarm.
Recipe courtesy Jacques Pepin, The Apprentice, Houghton Mifflin Company, 2003