Peel the chilled eggs, removing all of the shell and membrane. Using a sharp knife, divide each egg in half lengthwise. Remove the cooked yolk from the egg and place in a bowl. Repeat until all of the eggs have been prepped in this manner.
Using a large fork, break up the egg yolks. Add the softened butter and continue using the fork to work the yolks and butter into a smooth paste. Add the mayonnaise and mustard and mix until smooth. Taste for seasoning, adding salt and pepper if desired. If you prefer, white pepper can be used to keep from creating black specks of pepper in the bright yellow yolk mixture.
Using a small spoon or a pastry bag with a large tip, fill the hollow egg whites with the yolk mixture. You can top each egg with a sprinkling of paprika for color or add a bit of fresh minced herbs from the garden. We tried fresh dill, thyme, and chive and loved the burst of fresh flavor they each added to the deviled eggs.
Deviled eggs are best eaten within an hour or two of assembling, so serve them immediately and enjoy every last bite!