Why learn to make mayonnaise when it's so affordable and easy to find at the market? For beginning cooks this is not a rhetorical question. If you've not done it before, binding oil with water can be as intimidating as making your own water from hydrogen and oxygen. But after students actually make their own mayo and taste it alongside store-bought (I keep a jar on-hand just for this purpose) they're forever sold on the homemade variety.
The sheer pleasure off making an emulsified sauce never wears off. I always feel like a wizard in the kitchen when I make mayonnaise. It still amazes me how that a single egg yolk will absorb a copious amount of oil once it's been primed with a little mustard and vinegar. All you have to do is pour the oil in very slowly at the start and whisk the mixture into a thick, glossy, delicious condiment. And what if the worst happens, and it breaks down into a curdled mess? Don't throw it out! Get a clean bowl, spoon in a tablespoon of the "broken" sauce, add a teaspoon more mustard and vinegar and very slowly whisk in the remaining sauce.
Mayonnaise is one of those 'mother' type sauces that invites improvisation. My favorite variation, sauce gribiche, combines sieved hard boiled egg yolks, chopped capers, diced cornichon pickles and fresh herbs with the basic formula of raw yolk, mustard and vinegar. 'Gribiche' is a Dutch word used to describe a foul-tempered wife (biche in French is a female deer). Sound like a slur in English doesn't it? Perhaps that's why Julia Child chose to call it tartar sauce in volume I of Mastering the Art, Sauce gribiche is sometimes confused with sauce ravigote, in which cornichons and capers are folded into a vinagrette.
In France sauce gribiche is traditional served with tête de veau (calf's head) a rich gelatinous dish benefits from this sauce's acidity and textural interest. Here in the States, I pair it with roasted and grilled seafood such as cod, salmon or shrimp. Gribiche is also a novel dipping sauce with crudites or a buffet of steamed summer vegetables. A cautionary word: as a stand-in for mayo in a sandwich, sauce gribiche is absolutely habit-forming.