Separate the egg yolk from the egg white and whisk the egg in a bowl.
Add the mustard and whisk together.
Gradually and very slowly add about half the oil, whisking continuously for around 3-5 minutes, or until thickened. Whisk the vinegar, this will loosen the mixture slightly and give it a paler colour.
Continue to gradually add the remaining oil, whisking continuously.
Season with a pinch of salt, cayenne powder and a little more vinegar, if needed.