With a thumbtack poke a hole at the bottom of the egg to relieve pressure during cooking.
Place eggs in a large sauce pan and cover with cold water. After it starts to boil count 13 minutes.
Remove the pan from the heat and immediately change the water to cool the eggs quickly.
Lightly tap the entire surface of the egg on a rigid surface until cracking the entire shell.
Peel the eggs in running water starting at the base
Carefully cut the eggs in half and transfer the yolk to a bowl.
Add to yolks mustard, mayonnaise, vinegar and/or horseradish, salt and black pepper.
Mix well with a fork or blender until smooth.
Transfer the egg yolks to a pastry bag and pipe into egg whites.
Garnish with paprika, cover and store in refrigerator until serving time.
You can also garnish with olives, bacon, chives, you choose.