Hard-boil the eggs (see notes for tips).
MEANWHILE, prepare a platter to place the finished eggs on. Eggs will slide right off of a plate so it is best to lay out some decorative lettuce or something similar that will help keep them in place. (Alternately, use a deviled egg serving plate that has divots for each egg)
When eggs are done cooking, immediately put them into cold water and let them cool completely.
Carefully peel the eggs (discarding the shells or putting them in the compost bin).
Cut eggs in half lengthwise.
Gently scoop out the yolks into a medium bowl. Place the egg white halves onto the prepared platter or deviled egg holder, hollow side up.
Place the olive into the hollow of one of the eggs. (Note - I don't recommend doing more than one; they are meant to be a surprise but they are not... the most delicious.)
Mix mayonnaise, mustard, and salt into the egg yolks, combining thoroughly.
Use a pastry bag to pipe the filling into the egg hollows, completely covering the olive in the surprise egg so it looks like the rest. (Or just dollop the filling in using a spoon for a more rustic look).
Sprinkle paprika lightly over the tops. Be gentle with this; a little goes a long way. Add parsley, if desired.
Decide whether to let the guests know that the dark one’s eyes may be on them.