Prepare the Hard-boil the eggs, boiling the eggs for “exactly eight minutes"..
Cool them in an ice bath, peel, and slice in half lengthwise.
Remove the yolks and place in food processor and chop fine.
Add the mayonnaise, melted or softened butter, salt and pepper and chopped dill until smooth and creamy.
Taste for seasoning.
Put a mixture in pastry bag with a large star tip to pipe the filling neatly into the egg whites half.
Cover loosely with plastic wrap and refrigerate, up to 3 hours.
To serve, top each half egg with a few grains of red caviar.
Arrange on a thick bed of dill to keep the eggs from sliding, unless you have old-fashioned, deviled egg dishes, which are very decorative.
These are often served as part of a cocktail party menu, sometimes paired with other luxurious toppings like smoked salmon or capers.