Place the eggs in a small saucepan, cover with water and bring to a gentle boil. Cook for 9 to 10 minutes. Drain off the water, and shake the eggs in the 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.
Remove the egg shells, and cut them lengthwise. Scoop out the yolks and place them in a bowl, along with the garlic, parsley, milk, salt, and pepper. Mash with a fork to create a coarse paste. Spoon the mixture back into the hollows of the egg whites, reserving 2 to 3 tablespoons of the filling to use in the dressing.
Heat the vegetable oil in a nonstick skillet over medium until shimmering, 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.
For the Dressing: Mix all of the dressing ingredients in a small bowl with a whisk or a spoon until well combined.
Drizzle the warm eggs with the dressing, and serve lukewarm.
Fried deviled eggs Pépin was originally published on https://soupaddict.com/fried-deviled-eggs-pepin/