Place the eggs in a saucepan and cover with cold water. Bring to a boil, then reduce heat and simmer for 10 minutes. Drain the water, then let the eggs cool.
Peel the eggs, then cut in half lengthwise. Remove the yolks and place them in a bowl.
Mash the yolks with a fork until they are crumbly. Add mayonnaise, mustard, vinegar, salt, and pepper; mix until smooth.
Spoon or pipe the mixture into each egg white half.