Place egg yolk, vinegar, water, mustard and a pinch of salt in a tall jug (see note above for why). Pour in oil.
With your stick blender head on the bottom of the jug, blitz on high speed. As you start to see the emulsion forming, slowly raise the stick blender so the upper layers of oil get emulsified too.
Taste and season with extra salt if needed (this can help tone down any bitterness from the oil if using olive oil) or a little extra vinegar if the flavour is too flat.
If the mayo is too runny, carefully add oil in a thin stream while mixing with the stick blender. This requires some dexterity. If too thick, stir in a little water using a spoon, one tablespoon at a time.
If your mayo splits or doesn’t form a creamy, thick emulsion, it’s OK! Just start again with a new egg yolk, vinegar, water and mustard. Pour the split mayo on top in place of the oil and cross your fingers this time.