Put the egg, garlic, lemon juice, parsley, and green onions in a food processor and puree for 15 seconds. With the processor running, pour the oil through the feed tube in a steady stream. Add the cayenne, mustard, and salt and pulse once or twice to blend.
Cover and let sit for 1 hour in the refrigerator before using. Best if used within 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 food poisoning... 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 shell."