Gently crack the egg and slide the yolk from one half of the shell to the other to separate it from the white. It should remain intact throughout the process. Place the yolk in a bowl. Don’t throw away the white—you can use it for another recipe, such as meringues!
Crush the garlic cloves, peel them, remove the germ, and use a garlic press to mash them into a paste. Add them to the bowl. Season with salt and pepper.
Measure out the olive oil in a measuring cup and grab a whisk if you have the habit, stamina, and patience to whisk the aioli by hand. As for me, after a few minutes, I gave up and switched to an electric mixer with plastic beaters, which work well for this type of recipe.
Now comes the crucial moment: start by adding just a few drops of oil to the mixture in the bowl, and begin whisking. If you add too much oil right away, your aioli won’t set!
Once the ingredients are well combined with the oil, continue adding the oil very gradually until you have used half of it. The mixture must remain firm before you add any more oil.
You can go a little faster now, while continuing to beat vigorously.
Once all the oil has been added, pour in the lemon juice, give it a few stirs, and it's ready!