Aioli
My mini-processor: I've drilled a small hole through the plastic top of my spice grinder. A small enamel funnel fits tightly into this hole, so I can pour the olive oil in while the processor is running…and dressing is emulsified perfectly. To prevent a bit of a mess, I fold a paper towel and wrap that around the outside of the grinder base, before putting on the lid. If you don't have a similar set up, follow this same process in a small bowl and whisk like mad while pouring in the oil.
Place all ingredients except oil into the base of the mini-processor. Whiz together until well-combined, 15–30 seconds. With the processor running, add olive oil through funnel—the thinnest drizzle possible to get started, then increase to a slightly thicker stream.
Coddling your egg: There's some debate about whether this is necessary, but I figure why not play it safe? Bring a pan of water to a boil, set a timer, grab a small strainer-scoop. Boil the egg for 40 seconds, scoop it out, run under cold water, then use in aioli.