Place 6 large eggs in a pot and cover with cold water. Bring to a boil over high heat, then remove from heat and cover the pot tightly. Let them sit for 12 minutes—this is the secret to creamy yolks. After 12 minutes, drain and rinse with ice water until completely cool. I always use ice because warm eggs are harder to peel smoothly.
Once cooled, gently tap and roll each egg to crack the shell all over. Peel under running water, starting from the wider end where the air pocket is. The water helps separate the membrane from the white, making peeling way less frustrating. Take your time here—nobody wants shell bits in their deviled eggs.
Slice each egg in half lengthwise and carefully scoop out the yolks into a small bowl. Arrange the egg white halves on a serving platter, keeping the hollow side facing up. Pro tip: I like to arrange mine in a circle to make the presentation look intentional and pretty.
Add 1/2 cup mayonnaise, 1 tablespoon Dijon mustard, 1 teaspoon white vinegar, and 1/2 teaspoon sugar to the bowl with yolks. Mash everything together with a fork until smooth and creamy. Don't use a food processor or you'll end up with a weird grainy texture that nobody loves.
Stir in 1/4 teaspoon salt, 1/4 teaspoon black pepper, and 1 tablespoon finely chopped fresh dill. Taste the filling and adjust seasoning if needed—it should taste a little bit more seasoned than you'd normally want because the egg whites are pretty bland. This is where my 6-year-old tried one last Tuesday and ate three more before I could stop her.
Spoon or pipe the filling into each egg white half using a small spoon or pastry bag. I personally think piping makes them look more elegant, but honestly spoons work just fine and there's way less cleanup. If you're piping, just use a ziplock bag with one corner snipped off in a pinch.
Top each filled egg with a tiny pinch of smoked paprika, then add 1/2 teaspoon of the relish, a sprinkle of chopped chives, and a few extra dill pieces. Let them chill in the fridge for at least 30 minutes before serving. The flavors meld together better when they've had time to get cozy together in the cold.