Mixing by hand allows you to “feel” the mayonnaise as the oil is added and it begins to thicken. Pour in the oil very slowly, drop by drop at the beginning, until it begins to emulsify, then add the rest in a thin, steady stream. If added too quickly the mayonnaise will separate. Mustard and vinegar help stabilize and emulsify the mayonnaise.
Stand a deep bowl on a tea towel to make it stable. Whisk the egg yolk mixture until evenly combined.
Whisk in the olive oil a drop at a time until the mixture thickens. Add the remaining oil in a thin stream.
Add the vinegar a little at time, whisking well after each addition to ensure it is completely mixed and emulsified. Check seasoning.