Place eggs in a large saucepan. Add enough water to cover eggs by about 1 inch. Bring water to boiling. Cover pan; remove from the heat. Let stand for 15 minutes.
Drain off water. Gently shake saucepan so that eggshells crack in several spots. Add enough cold water to the pan to cover the eggs; add about 3 cups of ice to the pan. Let eggs stand about 10 minutes or until cooled to room temperature.
Peel the eggs; rinse eggs with cold water. Place eggs in a medium bowl. Use a potato masher to coarsely mash the eggs. Add yogurt, mustard, salt, and pepper to eggs. Mash and mix until well combined and to desired consistency. If desired, stir in celery and dill.
Cover; chill in the refrigerator for at least 1 hour before serving. Store any leftover egg salad in a covered bowl up to 3 days.