Place eggs in a medium saucepan covered with cold water. Cover with lid and bring to a boil. Once boiling remove from the heat, leave covered for 15 minutes. Rinse under cold water until cool enough to handle. Peel and place in large bowl.
Finely chop eggs. When you think they're fine enough, chop them some more. Then add celery, scallions, mayonnaise, salt and pepper. Mix until well combined. Adjust seasoning as needed. Chill until ready to serve.