Garlic Mayonnaise

In Catalonia in the north of Spain where aioli is traditionally found, it is a simple triumvirate of garlic, olive oil, and salt. (There it is spelled allioli or alioli in Catalan or Spanish, respectively, and literally translates to "garlic and oil.") There are no eggs to speak of in the preparation; the garlic is minced to oblivion in a mortar and pestle and the oil is incorporated slowly, until a beautifully opaque emulsion forms. This is similar to Toum, a Lebanese sauce of garlic, oil, salt, and lemon juice. 

Homemade mayo is a combination of egg yolks, vinegar, oil, and lemon juice. Making mayonnaise  is a matter of creating an emulsion of egg yolks and oil. The acid in the vinegar does more than add flavor—it increases the amount of oil the egg yolks are able to absorb, which makes the emulsion more stable and less easy to mess up. But those acidic ingredients are also essential flavor-wise. Egg yolks and oil are both ingredients with relatively mild flavors, so the vinegar and lemon juice and the vinegar in the Tabasco and mustard help wake things up.

A light, neutral oil like safflower or canola oil will give the best results, but once you've mastered the technique, you can start experimenting with oils that have more distinctive flavors, like walnut oil, avocado oil, or hazelnut oil. Olive oil is not recommended as its flavor will overpower the rest of the ingredients.