Put eggs in a large saucepan and cover with water. Cover pot and boil 10 minutes. Drain and rinse with very cold water to cool quickly.
Mix mayonnaise, mustard, and vinegar in a small bowl. Peel eggs, then slice in half. Separate yolks from whites and put whites on a serving plate. Stir yolks into mayonnaise mixture. Gently mix in olives and capers.
Fill whites with yolk mixture. Sprinkle tops with parsley.
Note: Nutritional analysis is per 2 half-egg serving.