In a bowl or the container provided with your immersion blender, combine the garlic, lemon juice, balsamic, salt, and egg yolks.
Place the immersion blender in the bowl and process in short pulses until smooth. With the motor running, add the olive oil in a slow, steady stream and process until smooth and blended. Season with salt and pepper.
Transfer the aioli to a small bowl, cover and refrigerate until ready to serve.
Makes 1-1/2 cups.