Place eggs in a saucepan and cover with cold water by at least an inch. Bring water to a gentle boil, then remove from heat, cover, and let sit for exactly 10 minutes.
Transfer eggs to an ice bath immediately to stop the cooking process. Let cool for at least 5 minutes before peeling.
Peel the eggs carefully, then chop them into your preferred consistency.
In a medium mixing bowl, combine the mayonnaise and Dijon mustard. Add salt and freshly ground black pepper to taste.
Gently fold in the chopped eggs, diced celery, and sliced green onions.
If using optional ingredients like dill, paprika, bell pepper, capers, or garlic powder, fold them in now.
Taste and adjust seasoning as needed.
Cover and refrigerate for at least 30 minutes to allow flavors to meld together.
Serve the egg salad on crisp lettuce leaves or as a sandwich filling.