Step 1: In a medium bowl, combine the egg yolk, minced garlic, Dijon mustard, lemon juice, salt, and pepper. Whisk vigorously until the mixture is well combined and slightly pale.
Step 2: For the traditional method, slowly begin to add the olive oil, literally drop by drop, while whisking continuously and vigorously. This is crucial for emulsion.
Step 3: As the mixture starts to thicken and emulsify into a creamy consistency, you can gradually increase the olive oil to a very thin, steady stream, continuing to whisk constantly.
Step 4: Continue whisking until all the oil is incorporated and the aioli is thick, smooth, and creamy. If using an immersion blender, combine all ingredients in a tall, narrow jar, place the blender on the bottom covering the yolk, turn on high for 15-20 seconds, then slowly lift upwards.
Step 5: Taste the homemade garlic aioli and adjust seasoning if necessary. You might want more salt, lemon juice, or a tiny pinch of extra garlic (be careful, raw garlic can be strong).
Step 6: Transfer the garlic aioli to an airtight container. Refrigerate for at least 30 minutes before serving to allow the flavors to meld. This garlic aioli recipe is best consumed within 5-7 days.