First, cook the hard-boiled eggs. Fill a medium saucepan with water and bring to a boil. While the water heats up, fill a bowl with water and plenty of ice cubes and set aside. Use a spider or slotted spoon to slowly drop the cold eggs in a single layer into the boiling water. Cook the eggs at a rolling boil for 14 minutes. Use the spider to immediately plunge the eggs into the ice water bath. Chill the eggs for 5 minutes. Remove the eggs from the water and remove the shells.

Slice the eggs in half lengthwise. Gently scoop out the yolks into a bowl and reserve the egg white halves. Use a fork to mash the yolks fine. Add the mayonnaise, mustard, lemon juice, Old Bay, and kosher salt. Mix well. Use the back of a spoon to mash well, pressing the yolks against the side of the bowl until extra smooth. Pipe or spoon the egg yolk mixture into the egg whites. Sprinkle with paprika and minced chives. Eggs can be refrigerated for up to 3 days.