Place eggs in a large pot, and fill with enough cold water to cover the eggs by 2 inches.
Place pot over high heat, and bring up to a rolling boil. Cover, remove from heat, and let stand for 15 minutes.
Drain eggs, and fill pot with ice water to cool down. Let cool for at least 5 minutes.
Peel and halve eggs, scooping the yolks into a mixing bowl or food processor and placing the whites on a serving platter as you go.
Mash together (or food process) the egg yolks, mayonnaise, relish, yellow mustard, and pepper.
Lightly sprinkle the entire platter of egg white halves with salt before filling each with an equal amount of the yolk filling. Refrigerate for at least 30 minutes before serving. Garnish with a sprinkling of paprika and chopped fresh chives, if desired.
HELPFUL TIP: For the best presentation, use a pastry bag with a star-shaped tip to pipe the yolk filling into the whites.