Place eggs in a pot and cover with cold water, adding the white vinegar to help prevent the shells from cracking. Bring to a boil over high heat, then remove from heat, cover, and let sit for 10 minutes. This gentle carryover cooking ensures perfectly cooked yolks without that gray-green ring around the outside. Transfer eggs to a bowl of ice water and let cool for 5-10 minutes to stop the cooking process and make them easier to peel.
Once cooled, gently tap and roll each egg on the counter to crack the shell all over, then carefully peel under cool running water, working from the wider end where the air pocket makes separation easier. Pat the peeled eggs dry with a paper towel, then slice each one lengthwise with a sharp knife to create two equal halves.
Carefully remove the yolks from each egg white half and place them in a small bowl, keeping the whites arranged on a serving plate. Mash the yolks with a fork until smooth, then fold in the Miracle Whip and Dijon mustard until well combined and creamy. Season with a pinch of salt and black pepper, tasting and adjusting as needed—I find that the mustard is already quite flavorful, so I go easy on the salt to avoid oversalting.
Spoon or pipe the yolk mixture generously into each egg white cavity using a small spoon or piping bag—I prefer using a piping bag for a more elegant presentation. Sprinkle each filled egg with paprika for color and a subtle spice, then add a small dollop of relish on top for a tangy crunch that complements the creamy filling perfectly.