Place the egg, lemon juice, Parmesan, green onions, garlic, buttermilk, salt, and pepper in the bowl of a food processor and process on high speed for 30 seconds.
With the motor running, add the oil through the feed tube in a slow, steady stream and process until it forms an emulsion.
*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."