First hard boil the eggs: Fill up a large saucepan half-way with water and gently add the eggs. Cover the eggs with at least an inch of water. Add a tsp of vinegar to the water (this will help contain egg whites from leaking out if any of the shells crack while cooking).
Bring the water to a rolling boil. Cover, and remove from heat. Let sit covered for 15 minutes.
Drain hot water from pan and run cold water over the eggs. Add some ice to help in the cooling process. It doesn't hurt to shake the pan with the ice and eggs in it and let the shells crack a bit. This will just help them to peel easier. Let sit in the cool water a few minutes, changing the water if necessary to keep it cool.
Peel the eggs.
Slice each egg in half, lengthwise. Gently remove the yolk halves and place in a small mixing bowl. Arrange the egg white halves on a serving platter.
Using a fork or a hand mixer, mash up the yolks and add Dijon mustard, mayonnaise, onion, tabasco, and season to taste with salt and pepper.
Spoon egg yolk mixture into the egg white halves. You can also put the filling into a resealable bag, snip the corner off and fill the shells that way. Garnish with chopped parsley.