Start by whisking the egg yolk in a bowl. Then slowly dribble half the oil into the yolk while whisking for 5 minutes.
After 5 minutes of whisking the yolk and oil, add the vinegar and whisk again until combined. This will thin out eh mixture slightly.
Continue to dribble in the remaining oil while whisking for another 5 minutes. Add the salt and mustard before a final whisk together.
Transfer to a clean, sterile storage container and keep in the fridge for up to 1 week.