Hardboil and shell the eggs. Cut the eggs in half (I keep a paper towel around to wipe the yolk off of the knife between cuts to make cutting easier). Place the yolks in a bowl and set the whites aside.
Finely mince the shallot(s).
Using a fork, crush the yolks until they are fine.
Combine the yolks, shallot, mayonnaise, mustard, vinegar, salt and pepper and stir until smooth. I add the ingredients a little bit at a time and periodically taste to get the flavor to where I want it.
Place the yolk mixture in a Ziplock bag. Cut a corner off the bag and pipe the yolk mixture onto the egg whites.