Place egg, mustard, vinegar, sugar, pepper and salt in a food processor (or bowl for immersion blender). Blend for 30 seconds.
Then with food processor switched on, add oil in very thin stream ( through the hole provided in processor for this purpose, if not stop processor at intervals and then add little oil each time and continue to blend). When mayonnaise start to thicken add all remaining oil little at a time.
Your mayonnaise is ready.
Store in fridge in air tight container and use within 5 days, the mayonnaise is good until it smells and tastes good.