With Kalamata olives and garlic flavoring the yolk, these deviled eggs have a Mediterranean flavor.
In a medium saucepan, cover eggs with 1 inch of water. Bring to a boil; remove from heat. Cover and let stand 12 minutes. Drain eggs; run under cold water until cool enough to handle.
Peel and halve eggs lengthwise; remove yolks and transfer to a bowl. Mash with a fork; mix in mayonnaise, mustard, and vinegar. Press through a sieve to make smooth. Pulse yolk mixture with olives and garlic in a food processor.
Using a pastry bag fitted with desired tip (we used plain and star tips), pipe yolk mixture into whites. Garnish with olive slivers. Serve immediately, or chill up to 2 hours.
Instead of piping the filling with a pastry bag and tip, you can use a resealable plastic bag with a corner snipped off. Or simply spoon it into the egg whites.