Fill a large pot halfway with water and bring to a boil. See note 1 below.
Arrange eggs in steamer basket, if using. Lower basket into water. Or use a spider strainer or large spoon to gently submerge eggs a few at a time until you've added them all.
Set a timer for 12 minutes.
When the water begins to bubble vigorously again, reduce heat to maintain a gentle simmer so the eggs don't jostle around too much.
While the eggs cook, fill a large bowl halfway with ice water.
When timer rings, pull eggs out of pot and plunge into ice water.
Cool for 15 minutes.
Peel carefully and give a quick rinse under running water to remove any remaining bits of shell. Dry well and chop.
Finely dice the celery and finely mince the shallot.
In a large mixing bowl, stir together the mayo, mustard, vinegar, salt, and pepper until smooth.
Add the chopped eggs, celery, and shallot and stir gently but thoroughly until well combined.
At this point, stir in any additional ingredients, if using. Refer to the post section above to learn more.
Right before serving, place salad into a serving bowl and sprinkle with as much paprika as you like.