Step 1

Bring a medium pot of water to a boil. Submerge the eggs in the boiling water with a slotted spoon and adjust the heat to maintain a gentle simmer. Cook for 10 minutes, then drain off the hot water and run the eggs under cold water until cooled.

Step 2

Peel the eggs and prick them all over with a fork, being careful not to go deeper than the white layer. Place the eggs in a bowl or jar and cover completely with the pickle brine. Cover and refrigerate overnight.

Step 3

Cut the pickled eggs in half (reserve the brine). Pop out the yolks and transfer them to a medium bowl. Finely chop the egg whites and reserve (see Cook’s Note).

Step 4

Add 2 tablespoons of the reserved pickle brine to the yolks and mash them together with a fork to a chunky paste. Add the mayonnaise, dill, mustard, cayenne, a pinch of salt and a generous grinding of pepper. Stir together until combined. Stir in the pickles and reserved chopped egg whites. Taste and season with more salt and pepper if needed. Sandwich on rye bread, if desired.