Place eggs in a saucepan and cover with cold water by one inch; bring to a boil, then reduce heat and simmer for 6-8 minutes, or until desired doneness.

Drain and cool the cooked eggs in an ice bath, then peel and chop them coarsely. In a medium bowl, combine the chopped eggs, mayonnaise, mustard, celery, and green onion, mixing well.

Season the egg salad with salt and pepper to taste; serve immediately or chill for later use.