Raw-yolk emulsions
How a yolk turns oil into a dressing, why the oil goes in slowly, and what to do when it splits.
Mayonnaise, aïoli and a proper Caesar dressing are one technique. A yolk is suspended between oil that wants to stay separate and water that wants to stay separate, and it holds the two together well enough to make something thick out of two thin things.
What the yolk is doing
Egg yolk carries lecithin and a set of proteins that are attracted to water at one end and to fat at the other. Whisked into a small amount of liquid, they coat each droplet of oil as it arrives and stop the droplets merging back into a pool. The dressing thickens not because anything has been added to it but because the oil has been broken into so many droplets that they can no longer move past each other freely.
That explains the two rules that otherwise sound like superstition.
Why the oil goes in slowly
A yolk can only coat so much surface at once. Poured in as a stream, the oil arrives faster than it can be broken up and coated, the droplets meet, and the mixture stays thin and greasy; it never emulsifies rather than splitting later.
So the first oil goes in a few drops at a time, and only once the mixture has visibly thickened and taken on a pale gloss can the pace increase. Past that point the emulsion is established and fairly robust.
Why there is always acid first
Lemon juice or vinegar goes in with the yolk, before any oil. It supplies the water phase the emulsion needs (an emulsion of oil in almost nothing has nothing to be suspended in), and it thins the yolk enough to whisk freely. A dressing built on yolk alone seizes.
Rescuing a split one
A broken emulsion has not been destroyed, only separated, and every ingredient in it is still good. Start again in a clean bowl with a fresh yolk, or with a spoonful of the acid, and whisk the split mixture into it slowly, exactly as if it were the oil. It re-emulsifies almost every time.
The raw-egg question
These dressings are not cooked, and the yolk stays raw. Where that matters (pregnancy, very young children, anyone immunocompromised), pasteurised eggs behave identically and are the straightforward answer. Some traditional versions use an egg dropped into boiling water for a minute, which barely changes it: a coddled egg is not a cooked one.