Place eggs in a single layer in a medium saucepan and cover with at least 1 inch of cold water.
Bring the water to a rolling boil over high heat.
Once boiling, immediately turn off the heat, cover the pan, and let the eggs sit in the hot water for 15 minutes. This gentle cooking method prevents overcooking and that unappealing green ring around the yolk.
Transfer the eggs to an ice bath or rinse under very cold water until they are cool enough to handle. Gently crack the shells and peel them, preferably under cool running water to help loosen the shell.
Slice each egg in half lengthwise. Carefully scoop out the yolks and place them in a small bowl.
Using a fork, mash the yolks into a fine crumble.
Add the mayonnaise, dill relish, and mustard.
Continue to mash and stir until the mixture is smooth and creamy.
Season with salt and pepper to your liking.
Evenly spoon or pipe the yolk mixture back into the egg white halves.
Garnish with a sprinkle of paprika, if desired.
Refrigerate until ready to serve. The eggs can be stored in an airtight container in the refrigerator for up to 3 days.
