In the bowl of a food processor or blender, add the Creole mustard, green onions, horseradish, garlic, mustard, hot sauce, Worcestershire, lemon juice, egg, salt, and pepper. Process until smooth, about 30 seconds.
With the motor running, slowly pour the vegetable oil into the blender or food processor in a slow, steady stream. Add the parsley and pulse to combine. Transfer to a container, fold in the chopped eggs and capers, cover, and refrigerate for 1 hour before using. This sauce will keep, refrigerated, for up to 24 hours.
*RAW EGG WARNING
The American Egg Board states: "There have been warnings against consuming raw or lightly cooked eggs on the grounds that the egg may be contaminated with Salmonella, a bacteria responsible for a type of foodborne illness. Healthy people need to remember that there is a very small risk and treat eggs and other raw animal foods accordingly. Use only properly refrigerated, clean, sound-shelled, fresh, grade AA or A eggs. Avoid mixing yolks and whites with the shellÖ"
Yield: 1 1/2 cups