Prepare the Garlic: Peel and finely mince the garlic cloves. Optionally, you can mash the garlic into a smooth paste using a mortar and pestle.
Whisk the Egg Yolks: In a medium-sized bowl, whisk the egg yolks together with Dijon mustard and lemon juice until the mixture is smooth and slightly pale.
Slowly Add Olive Oil: Gradually add the olive oil to the egg yolk mixture, very slowly at first, while whisking continuously to allow for proper emulsification.
Season the Aioli: Once the aioli has thickened, season with salt and white pepper to taste. Adjust seasoning as needed.
Chill and Serve: For the best flavor, refrigerate the aioli for 30 minutes before serving. This allows the flavors to meld and the garlic to mellow.