Place eggs in a large saucepan and cover with cold water by 1 inch. Bring to a boil and cook for 1 minute. Cover eggs with a tight-fitting lid and remove from heat; set aside for 8-10 minutes.
Cool eggs in a bowl of ice water for 2-5 minutes. Drain well and peel; cut the eggs in half lengthwise, reserving the yolks.
In a small bowl, mash the yolks with a fork until chunky. Stir in mayonnaise, relish and Dijon; season with salt and pepper, to taste.
Use a pastry bag to pipe into the eggs, garnished with chives and paprika, if desired.
Notes
Older eggs are easier to peel. Older eggs will generally be much easier to peel than fresh eggs. The higher pH of the older eggs allows the whites to separate from the inner shell membrane, making it that much easier to peel.
Use an ice water bath. Immediately cool the eggs in an ice water bath for 5 minutes, halting the cooking process and preventing overcooked yolks (and whites).
Try the IP for hard boiled eggs. Use the Instant Pot for the most perfect and easy-to-peel hard boiled eggs.
Make it lighter. Substitute plain Greek yogurt for the mayonnaise.
Use a pastry bag for the filling. A pastry or piping bag can help fill the egg whites uniformly and consistently with less mess and less time. Use a Ziploc bag with the corner snipped off as a DIY pastry bag. Use a piping tip (Ateco #846, a closed star pastry tip is used here) for more decorative patterns and a picture-perfect finish.
Mix it up. Add different garnishes, try an avocado version, skip the relish if it's not your thing, add a little bit of lemon juice to cut down the richness or add a dash of hot sauce to the mix.
Make ahead of time. The eggs can be hard boiled (and peeled) and placed in the fridge up to 24 hours ahead of time. The filling can also be made 1 day in advance and stored in a separate airtight container in the refrigerator. Be sure to let the filling come to room temperature for 15-20 minutes (as it may be too stiff) prior to filling the egg white halves.