Place the eggs in a saucepan and cover with water, about 2 inches higher than the eggs. Bring to a boil, cover with a lid, and remove from heat. Let the eggs sit undisturbed for 14 minutes. Run eggs under cold water until the shells are cool enough to handle.
Peel the eggs without damaging the flesh as much as possible. Slice them in half, and scoop out the yolks into a medium bowl.
Mash the yolks with a fork. Add mayonnaise, mustard, salt, and pepper. Mix and mash well until completely smooth (if desired, you can also process the filling in a food processor).
Using a spoon or a piping bag, fill each egg white half with deviled eggs mixture. Sprinkle with smoked paprika, and top with a leaf of parsley. Transfer to a serving platter and serve immediately.
Leftover deviled eggs will keep in an airtight container in the fridge for 3 days.