Hard-boil the eggs by placing them in a saucepan with enough water to cover them. Bring the water to a boil, and boil for 10 minutes. Use a large spoon to transfer the eggs to a colander, and place under cold running water to cool. Peel and set aside until ready to make the rest of the dish.
Halve each egg lengthwise, and pop the yolks out into a large bowl. Add the Homemade Mayo, onion, mustard, relish, and vinegar, and mix until smooth. Season with salt and pepper.
Spoon the yolk mixture into a piping bag (or just use a large resealable plastic bag and cut one corner off). Carefully fill each egg white half with the yolk filling.
