1 egg yolk 170 ml sunflower oil 2tbsp of French mustard 1 clove garlic, crushed (optional) Salt and Pepper 1/2tbsp white vinegar or lemon juice (optional)
Make sure all the ingredients are at room temperature before starting. Place a damp tea towel beneath the mixing bowl. Add the egg yolk and the mustard. Beat well with a whisk or fork for a couple of minutes Add salt and pepper (salt helps thicken the yolk) and whisk for 30 secondes. Pour in the oil in a very thin stream, whisking continuously until you have a thick, glossy sauce. Beat well between additions to avoid overwhelming the yolk and curdling the mixture. As the mixture thickens, start to add oil more quickly. Once the sauce is near the consistency you want it ( you may not need to use all the oil) Add garlic, vinegar or lemon juice (only at the end as it will thin out the egg yolk) Cover and keep refrigerated until you are ready to eat (can be stored refrigerated and covered for several days)
At the end of the process, you can stir any further ingredients such as chopped herbs or anchovy, curry powder or tomato paste.
I never used olive oil because I think this can be bitter and overpowering, if you adore olive oil I suggest to add a little extra virgin olive oil at the end.
Other method : You can use 1 whole egg and a food processor. The egg is mixed with mustard, salt and pepper and garlic if you wish, and then, with the motor still running, add a thin stream of oil. The result is less thick that the classic mayonnaise but it is quicker and very reliable. I found that this kind of mayonnaise is lighter than the classic one.
If your mayonnaise does turn on you, it can be rescued by starting again in a clean bowl and beating the curdled sauce, spoonful by spoonful, into the new mixture (egg yolk and mustard)