Place the eggs in a pot and cover with cold water.
Bring to a boil, then reduce to a simmer and cook for 9–10 minutes.
Transfer to an ice bath immediately to stop cooking and make peeling easier.
Peel the eggs carefully and slice in half lengthwise.
Scoop out the yolks into a mixing bowl.
Add mayonnaise, Dijon mustard, vinegar (or lemon juice), salt, pepper, and cayenne.
Mash until very smooth and creamy—use a whisk or fork, or process for extra smoothness.
Spoon or pipe the yolk mixture into the egg white halves.
Use a piping bag with a star tip for a neat and elegant presentation.
Sprinkle with paprika, chopped herbs, or your favorite toppings.
Serve chilled as a classy appetizer or snack.
