Place the egg, 1 teaspoon of mustard, 1 tablespoon of lemon juice and salt in a pouring or measuring jug. If you don’t have one, use something that is tall with a thin base so the blades of the immersion blender can easily emulsify the oil and egg. Don’t use a bowl or something with a wide base here.
Add the oil and allow everything to settle for a minute or two.
Place your immersion blender in the measuring jug, flush with the bottom. Begin to blend, holding the immersion blender in the bottom of the jug. When the mixture in the bottom of the jug starts to turn white and thick (like, say, mayo) slowly pull the immersion blender upwards while continuing to blend. Continue until you reach the top – the whole jug should be fully emulsified thick mayonnaise. Continue to blend until there is no separated oil. This whole process of blending and emulsifying only takes about 30 seconds.
You can add the garlic and continue to blend, but I like little chunks. I use a garlic crusher and simply stir the garlic into the mayonnaise.
Taste and adjust for seasoning. Add the extra teaspoon of mustard and tablespoon of lemon juice here if you feel it needs it/to suit your tastes. If the aioli has gone too far in the salty or sour direction, add a tiny amount of maple syrup or sweetener to even things out.
Store in an airtight container in the fridge and eat within a few days.