Cook the eggs. Place eggs in a large saucepan and cover them with 1 inch of cold water. Bring the water to a boil over medium heat. Once the water has reached a boil, turn off heat, cover pot with a lid, and let stand for 12 minutes. Once 12 minutes has passed, place eggs in an ice water bath for 10 minutes. Peel and chop the eggs.
In a bowl, mix together the mayonnaise, celery, mustard and hot sauce. Fold in the eggs and season to taste with salt and pepper.