Shape a damp kitchen towel into a ring on your counter and nestle your medium mixing bowl inside. This will keep your bowl steadier while working.
Measure out your 1/2 cup of olive oil in a glass measuring cup with a spout and set aside.
Into your bowl add your 1 egg yolk and your 1/4 tsp kosher salt.
Using a micro plane or the smallest holes on a box grater, grate your garlic cloves into the egg yolk. You want to wither grate or make a paste of the garlic so it incorporates smoothly, If you would rather use a knife, smash your minced garlic with the side of your knife and drag across your cutting board before adding to the egg yolk.
Now we emulsify. Whisk the egg yolk mixture brefly to combine well. Add olive oil a few drops at a time while whisking continuously, As the aioli begins to emulsify, increase the oil to a steady light stream. Keep whisking continuously.
When all the oil has been added, whisk to fully incorporate. Add 1 teaspoon of freshly squeezed lemon juice and whisk briskly to combine, Taste and add more salt and lemon juice if needed to suit your preference.