The shell of fresh eggs is tightly attached to the egg itself whereas older eggs the white inside has started to pull away from the shell, making them easier to peel. When peeling begin at the large end; with an older egg there will be a little air pocket there making it easier to get away from the white.
To hard boil, arrange eggs into a saucepan and cover with cool water. Over high heat bring to a boil and immediately turn the heat off and cover the eggs for 15 minutes.
Prepare an ice bath, a large bowl that will hold all the eggs, fill with ice and when eggs have finished cooking drain off the hot water and place eggs into the ice, cracking a bit of the shell as you do. Cover with cool water and let stand until completely cooled, 20 minutes or so. This step can be done a day ahead of time, after eggs have cooled refrigerate until ready to use.
Cut eggs in half lengthwise with a chef’s knife, not a serrated knife. Pop out the yolks into a mixing bowl. If you don’t have a plate for deviled eggs you can shred some radicchio or dark red lettuce onto a serving plate. If using the lettuce, slice a tiny piece from the round end of the egg so it doesn’t roll. Arrange egg whites cut side up on the lettuce.
Mash yolks with fork then stir in mayonnaise, mustard, and vinegar. Mix ingredients together well. Add sea salt and pepper, to taste. If the yolks aren’t creamy enough add a little more mayonnaise. You can also adjust the mustard and vinegar to taste.
Place the mixture into a pastry bag or a plastic storage bag, snip a diagonal piece from the bottom corner of the storage bag and use as a piping bag. Pipe the yolk mixture or spoon into each egg white half, dividing evenly as possible between the eggs.
Sprinkle eggs with paprika and/or minced chives if desired. Serve immediately or refrigerate until ready to serve. If refrigerating, you’ll want to cover with plastic wrap; place toothpicks into egg whites around the outer edge of the plate and in the center to make a ‘tent’ with the plastic wrap so it doesn’t touch the egg yolks.