Put the egg, tequila, and garlic in a blender, cover, and puree until smooth. Slowly drizzle in 1/2 cup of the olive oil through the feed tube in the top of the blender in a slow but steady stream, until mixture begins to emulsify. Add the lime juice and continue drizzling in the remaining olive oil. Turn the blender off, add the cilantro, salt, and pepper, and pulse to incorporate. Chill if not using immediately.
*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."