From America's Test Kitchen
Oil-based sauces like mayonnaise often separate into their component parts, with the oil forming an unattractive pool on top of the other ingredients. Egg yolks contain a natural emulsifier, which first helps bind the ingredients and then prevents them from separating. Like most other contemporary “aioli” recipes, ours calls for two egg yolks. But we wanted to guarantee that our garlic mayonnaise would stay together. We began looking for another natural emulsifier that would not muddy the sauce’s fresh garlicky lemon flavor. Mustard is not a traditional ingredient, but we found that just a bit of it further emulsified the mixture and added a pleasant hint of acidity.
We had been using a food processor in our initial tests because its mechanical agitation forms a much more stable emulsification than most cooks can achieve by hand. However, our aïoli had a slightly bitter taste. We were puzzled until we remembered a recent test kitchen discovery: Extra-virgin olive oil tends to become bitter in food processors, because it contains bitter-tasting compounds that break into small droplets at high processing speeds and become more prominent. The solution is to drizzle vegetable oil into the food processor just until the mixture emulsifies. At that point you can transfer the sauce to a bowl and whisk in extra-virgin olive oil by hand.
Makes about 1 1/4 cups