Whisk the yolks with the mustard and vinegar until well amalgamated in a clean bowl. Very slowly, drop by drop, begin adding the oil. The egg yolk mixture needs to accept the oil so If you are too quick the correct amalgamation won’t happen and the mayonnaise will remain split.
So, start gently. The sauce will thicken as you add more oil. As It does you can speed up the oil into a stead