Prep the ingredients for your aioli. First, finely mince the garlic, then squeeze the lemon juice into a bowl, making sure there are no seeds inside.
Add the garlic, lemon juice, egg, egg yolk, Dijon mustard, and salt to a deep cup. Using an immersion blender, slowly blend the ingredients until smooth.
Gradually pour in the oil, ¼ cup at a time, and blend with the immersion blender.
After a couple of minutes of blending, the mixture will become very thick and emulsified. At this point, add the pepper, stir, and serve.