This is an emulsion sauce that is best made by hand in a bowl, preferably a narrow, tallish one, using a wire whisk or wooden spoon. It should take about 5 minutes to make 500ml if the ingredients are at room temperature. The key to success is to add the oil slowly, adding more oil once the previous amount has been absorbed.
Put 2 egg yolks into a bowl with a Β½ teaspoon salt, some pepper and 1 teaspoon Dijon-style mustard, if desired. Combine with a whisk, then gradually add the first addition of oil, initially drop by drop and then in a thin, steady stream. When the ingredients look emulsified, that is, the mixture looks smooth, add some more oil. Continue with 300-400 ml oil, using about one-third extra virgin olive oil to two-thirds grapeseed or other vegetable oil. The mayonnaise should be quite thick and have a dull sheen by now. Acidulate to taste with lemon juice or white-wine vinegar, then correct the seasoning to taste. Refrigerate the mayonnaise in a sealed container with a piece of plastic film or greaseproof paper placed directly on the surface of the sauce. It should keep for at least 1 week.