Peel and finely mince or press the garlic cloves using a garlic press. This step is crucial as it releases the oils and flavor from the garlic, which is the base of the aioli.

In a mixing bowl, combine the egg yolk and Dijon mustard. Whisk them together until fully blended. This mixture acts as an emulsifier, helping to combine the oil and egg yolk into a creamy sauce.

Add the minced garlic, lemon juice, salt, and black pepper to the egg yolk mixture. Whisk until well combined. The lemon juice not only adds flavor but also helps to stabilize the emulsion.

While continuously whisking, slowly drizzle in the olive oil. Start with just a few drops at a time, gradually increasing to a thin stream as the mixture begins to thicken. This slow incorporation is key to creating a stable emulsion.

Continue whisking until all the oil is incorporated and the aioli is thick and creamy. If you prefer a smoother texture, you can transfer the mixture to a food processor and blend until desired consistency is reached.

Taste the aioli and adjust seasoning if necessary, adding more salt, lemon juice, or pepper to suit your preference.

Transfer the aioli to a serving bowl and enjoy it as a dip for vegetables, a spread for sandwiches, or a sauce for grilled meats.