Place eggs in a medium saucepan and cover with cold water by 1 inch. Bring to a boil over medium-high heat, then immediately remove from heat, cover, and let stand for 9-12 minutes.
Transfer eggs to an ice bath to stop cooking. When cool enough to handle, peel and chop into ½-inch pieces. Set aside.
Cut the avocado in half, remove the pit, and scoop the flesh into a bowl. Dice into approximately ½-inch cubes.
In a separate bowl, whisk together mayonnaise, Dijon mustard, lemon juice, salt, and pepper until smooth.
Combine the chopped eggs and diced avocado in a medium bowl. Add any optional ingredients (celery, red onion, herbs) if using.
Pour the dressing over the egg and avocado mixture. Gently fold everything together with a rubber spatula until evenly coated, being careful not to mash the avocado.
Taste and adjust seasoning with additional salt, pepper, or lemon juice if needed.
For best results, cover and chill for 15-30 minutes to allow flavors to develop. Garnish with chopped chives before serving.