You can use a food processor, or a mortar and pestle, or a bowl and wooden spoon. Some use vegetable oil rather than olive oil for a gentler result, I do not do this.
Your mayonnaise should have that bitter olive taste. Some thin with water; I feel this should be avoided.
3 Egg Yolks
1 Generous Teaspoon Dijon Mustard
2 1/2 c. Extra-Virgin Olive Oil (about)
A Healthy Splash of Lemon Juice
A Healthy Splash of White Wine Vinegar
Freshly Ground Black Pepper
Place the egg yolks, mustard, and a gesture of salt in a food processor, mix, then drizzle oil in very slowly; doing this will create the emulsion needed.
Add up to 2 1/2 cups oil; if you feel confident that the emulsion will hold, add more oil.
If it is getting too thick add a splash of lemon juice and white wine vinegar; you can always add more oil.
Season with salt.
After a while you will learn the various noises mayonnaise makes in the making that tells you when you have enough oil. These are hard to describe in words so I’m afraid you just have to listen to it. You want a consistency that has a body to it, but a body with give, not one that goes boing when you put a spoon in it.
If you are using a mortar and pestle, or bowl and spoon, follow the same process, but I stress the importance of the most gentle of drizzling of oil with this method.
This excerpt is taken from The Whole Beast by Fergus Henderson, purchase the book here