Pound and crush the garlic with a pinch of salt to a paste in a mortar, or chop finely using the flat part of your knife to crush the garlic and salt into a smooth paste. This may take a few minutes but it is essential that the garlic is perfectly smooth and that no chunks remain before starting to make the aioli. Transfer to a bowl, add the egg yolks and whisk to blend. Still whisking, slowly pour in a quarter of the olive oil, a few drops at a time, until the sauce starts to acquire some body, and then pour in the rest of the olive oil in a slow, steady stream, until it becomes a creamy thick sauce. To finish, add in the lemon juice, plus an extra squeeze of lemon juice to taste, and the hot water. Stir well and serve. If not serving right away, store in the refrigerator and consume within 2 days.
Ensure all of your ingredients are at room temperature to make this recipe. If you want to tame the flavor of raw garlic, blanch the garlic for a couple of minutes in boiling water or you can substitute sweet smoky roasted garlic, instead of raw. You can also add almost anything to flavor this aioli, like fresh herbs, other citrus juice, olive tapenade, sundried tomato paste, grainy mustard, miso paste (omit the salt in the recipe, if using miso) and even brandy.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.