Place the eggs in a pot and cover them with water. Bring the water to a boil, then remove the pot from heat and let the eggs sit covered for 12 minutes.
Drain the hot water and run cold water over the eggs until they cool. Peel the eggs and slice each one in half lengthwise.
Scoop the yolks into a mixing bowl. Add the mayonnaise, yellow mustard, white vinegar, salt, and black pepper. Mash everything together until smooth.
Spoon or pipe the yolk mixture back into the egg white halves. Slice each green olive into two rounds and place one round in the center of each filled egg.
Sprinkle the paprika lightly over the tops before serving.