Use very high quality, fresh eggs. Combine the egg yolks, whole egg, mustard, salt, freshly ground black pepper, and half of the lemon juice in a food processor. Process for 1 minute.
With the motor running, dribble in the oil in a slow steady stream. When you have added all the oil, shut the motor off and scrape down the sides of the bowl with a spatula.
Taste the mayonnaise. Correct the seasoning, if necessary; if you are using vegetable oil, you will probably need the remaining lemon juice.
Scrape the mayonnaise into a storage container, cover and refrigerate until ready to use. The mayonnaise will keep safely, if refrigerated, for at least 5 days. Let it return to room temperature before stirring and using.
