Add the eggs to a saucepot and cover with water. Place a lid on the pot and turn the heat on to high. Bring the water up to a full boil. Once it reaches a boil, turn the heat off and let the eggs sit in the hot water (lid on) for 12 minutes.
After 12 minutes in the hot water, transfer the eggs to an ice bath or run under cold water until cool. Peel the eggs then chop them into ½-inch pieces.
Add the chopped egg to a bowl along with the mayonnaise, Dijon, relish, lemon juice, salt, and pepper. Stir to combine, mashing some of the egg yolk into the dressing as you stir.
Taste the egg salad and adjust the ingredients to your liking. Serve immediately or refrigerate until ready to eat.