1. Roughly chop the eggs and place them in a mixing bowl. Add the salt, mustard, paprika, shallot, green onion, celery, and mayonnaise. Stir with a rubber spatula or a spoon until very well blended. Transfer to a container, cover, and refrigerate for at least 2 hours and up to 4 days.
2. Spread 1/4 to 1/2 cup of the egg salad between 2 slices of bread. Repeat with the remaining salad and bread.