Preparation

• In a mortar and pestle, make a paste of the garlic and 1/4 tsp. salt by pounding the cloves firmly with the salt. They’ll try to jump out of the mortar—don’t be concerned, because you’ll dominate and turn them into a paste. If you don’t have a mortar, then either finely mince the garlic with salt on a cutting board, or purée it in a small food processor or blender. You want a paste or a very fine mince.
• Stir or whisk the egg yolks and mustard into the garlic-salt paste. Then, add the neutral oil very slowly in a fine stream (ideally, in a plastic squeeze bottle) until the mixture becomes thick, whisking or stirring vigorously as you add the oil. A food processor or blender makes this easy to do, but you still need to add the oil very slowly. When the sauce gets very thick, stir in the lemon juice, then continue to add any remaining neutral oil, and then the olive oil. If you find that the aïoli becomes thicker than you like, add warm water 1 tsp. at a time until you reach the desired consistency. Season to taste with more lemon juice and salt.
• Aïoli is best served within 24 hours of being made, but it will keep for up to one week in an airtight container in the refrigerator.

Variations

• Caper Aïoli: With a silicone spatula, stir 2 Tbs. minced capers into 1/2 cup aïoli.
• Lemon Aïoli: With a silicone spatula, stir 1 tsp. finely grated lemon zest into 1/2 cup aïoli. Let the mixture sit for 30 minutes before serving so the flavors can meld.
• Basil Aïoli: With a silicone spatula, stir 1/2 cup fresh basil leaves, minced, into 1/2 cup aïoli.
• Tangy Aïoli: With a silicone spatula, stir 3 cornichons, diced, into 1/2 cup aïoli.