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 brisk 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.

Slice each egg in half lengthwise and carefully remove yolks to a medium bowl.

Mash yolks well with a fork.

Add mayonnaise, two tablespoons of the crème fraîche, mustard, salt, and pepper and continue mashing and blending until yolk mixture is creamy.

Stir in shallot. 

Using a piping bag fitted with a plain tip, a resealable plastic bag with one of the bottom corners snipped off, or a spoon, pipe or spoon the yolk mixture back into the egg halves.

Spoon about ½ teaspoon of crème fraîche onto each piece and top with a little bit of caviar. Garnish with a couple of snipped fresh chive pieces, and serve.