Halve hard-cooked eggs lengthwise and remove yolks. Set whites aside. Place yolks in a small bowl; mash with a fork. Stir in next six ingredients (through vinegar). Season to taste with salt and pepper.
Stuff egg white halves with yolk mixture. Cover and chill until ready to serve (up to 24 hours). If desired, top with tomato slices and/or thinly sliced basil.