Place the eggs in a single layer in a large saucepan and cover with cold water by 1 inch.

Bring to a full boil over high heat, then cover, remove from the heat, and let stand for 12 minutes.

Drain and transfer the eggs immediately to a bowl of ice water for 5 minutes, until cool enough to handle.

Peel the eggs under running water to help the shells release cleanly.

Slice each egg in half lengthwise and pop the yolks into a bowl, setting the whites cut-side up on a platter.

Mash the yolks with a fork until no lumps remain, then mix in the mayonnaise, mustard, and relish until smooth.

Taste and check the texture: the filling should hold a soft peak on the fork and taste bright from the mustard, not flat.

Spoon or pipe the filling back into the egg white halves, mounding it slightly.

Dust the tops with smoked paprika and chill for at least 15 minutes before serving, so the filling firms up enough to hold its shape.