In a mixing bowl, combine the egg yolk and Dijon mustard. Whisk them together until fully blended. This step is crucial as the mustard helps to stabilize the emulsion.

While continuously whisking, slowly drizzle in the olive oil. Start with just a few drops and gradually increase the flow as the mixture begins to thicken. This slow incorporation is key to creating a stable emulsion.

Once the aioli starts to thicken and emulsify, you can pour the olive oil in a steady, thin stream while whisking vigorously. Continue until all the oil is incorporated and the aioli is thick and creamy.

Add the minced garlic, lemon juice, salt, and black pepper to the aioli. Whisk until everything is well combined. Taste and adjust seasoning as needed.

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