Prepare all the ingredients.
Put the mustard in a bowl. the egg whites one after the other and mix the yolks with the mustard.
Season with salt and white pepper (preferably).
Whisk in a rotating pattern to mix egg yolks with mustard. Pour the oil in gradually.
The oil will combine with the mustard and eggs, making a mayonnaise. Keep whisking until all of the oil has been added.
At last, whisk vigorously to thicken the mayonnaise. Add the vinegar (optional). To be used within 24 hours.