In a mixing bowl, combine the egg yolk and Dijon mustard. Whisk them together until well blended. This forms the base of your aioli and helps emulsify the oil.

While whisking continuously, slowly drizzle in the olive oil. Start with just a few drops at a time to ensure the mixture emulsifies properly. This step is crucial as it creates a creamy texture.

As the mixture begins to thicken, you can gradually increase the oil flow to a thin stream while continuing to whisk. This should take about 3-5 minutes.

Once all the oil is incorporated and the aioli is thick and creamy, add the minced garlic, lemon juice, salt, and black pepper. Stir well to combine.

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

Transfer the aioli to a serving bowl. For best flavor, let it sit in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.