Combine the egg, lemon juice, lime juice, mustard, and onions in the bowl of a food processor or blender. Process on high speed until smooth. With the machine running, slowly add the oil in a steady steam, and continue to process until an emulsion has formed. Add the pepper sauce, salt, and cayenne and pulse for 10 seconds.
Pour into a decorative bowl and chill for 1 hour before serving.
Yield: about 1 1/4 cups
*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 shell…"