First the potatoes are peeled and cooked until soft for about 20 to 25 minutes. Let cool and cut into small cubes.
Now the olive oil is put into a tall, cylindrical vessel and the garlic cloves are pressed in with a press. Now add all the other ingredients. Rub in the lemon peel over a fine kitchen grater. Stir gently with the handle of a wooden spoon.
Now lower the hand blender to the bottom of the vessel. Let it run on the floor for about 10 seconds at the highest level and then slowly pull it up to the surface. Basically already done.
Then let it steep in the refrigerator for another 15 to 30 minutes and stir again.
If you use lime or orange instead of lemon (also with the peel), you can vary the aioli nicely. Just make sure that the amount of juice is about half a lemon.