If there's a fellow kitchen helper handy, ask her to assist either by holding the bowl steady while you whisk, or by slowly adding the oil while another hand whisks briskly. The transformation of ingredients is fascinating to watch, especially if you have the easy job!
1 egg yolk
1 teaspoon Dijon mustard
Juice of half a lemon
1 cup olive oil, or light, neutral oil such as grapeseed
1 teaspoon white wine vinegar
Salt and cayenne pepper to taste
Combine the yolk, mustard and lemon juice in a bowl and whisk together 15 seconds or so. Slowly (this is both the key and the trick!) begin to drizzle in the oil, keeping the stream slow and steady until an emulsification is established. You'll know by watching the side of the bowl, where you'll see “ribbons” collecting consistently on the edge. If the ribbon is fragmented or broken, or looks more like oil than a smooth, uniform mixture, add the oil more slowly. Once the mayonnaise appears to have stabilized, you can begin to add the oil more quickly again, until the entire amount has been incorporated.
Add the vinegar, salt and pinch of cayenne pepper. Adjust the seasoning, adding more lemon juice for acidity if desired. Store the mayonnaise in the refrigerator until ready to serve.
There are endless variations on this cold sauce, the most popular being aioli, which included the addition of a clove of garlic, finely minced or grated on a microplane. Finely minced herbs are another excellent addition.