Put egg yolks, mustard, lemon juice or vinegar and 1/4 cup of the olive oil in a bowl. Whisk to combine until it turns frothy. Add the remaining oil drop by drop at the beginning, then in a thin and steady stream. Whisk until absorbed.
Continue to whisk until the sauce emulsifies and thickens.
Add the sea salt, then adjust the taste with a little extra lemon juice or vinegar. Blend until the sauce is thick and smooth.
Turn into a clean bowl, cover and refrigerate until needed.