**Hard-boil the eggs:** Place eggs in a single layer in a saucepan and cover with cold water by about an inch. Bring to a rolling boil over high heat. Once boiling, remove from heat, cover, and let sit for 12 minutes. Drain hot water and immediately run cold water over the eggs until cool enough to handle. This helps prevent green yolks.

**Peel the eggs:** Gently tap the eggs all over on a hard surface to create cracks. Peel under cold running water for easiest peeling.

**Separate yolks and whites:** Carefully cut the eggs in half lengthwise and separate the yolks from the whites. Place the yolks in a medium bowl and the whites on a serving platter.

**Mash the yolks:** Mash the yolks with a fork until completely smooth.

**Mix in the other ingredients:** Add mayonnaise, mustard, vinegar, paprika, salt, pepper, chives, dill (if using), pickle relish (if using), and jalapeño (if using) to the bowl with the mashed yolks. Mix well until everything is thoroughly combined. If the mixture seems too thick, add a tablespoon of milk or cream for extra creaminess.

**Fill the egg whites:** Spoon or pipe the yolk mixture into the egg white halves.

**Garnish and serve:** Sprinkle with extra paprika and serve immediately or chill for later.