Whisk yolks in a mixing bowl. Pour oil very slowly into the bowl of whisked yolks. Pour only a few drops at a time whilst whisking constantly. With a bit of luck it will thicken eventually. When it is thickened we can put the oil a bit faster but still in a slow and steady stream. Whisk until oil has incorporated completely.
Keep whisking and adding the second half of the oil until the end. In case we have any failed attempts that didn't thicken or broke up then this is the time to use it.
Keep homemade mayonnaise in the fridge refrigerated. Use it up for about 6 days.