1. Place the aquafaba, apple cider vinegar, mustard, salt, and sugar in the bottom of a cup or jar that just fits the head of your immersion blender. Process on high speed until the aquafaba doubles in volume (about 1 minute).
Blender or food processor method: Place the aquafaba, apple cider vinegar, mustard, salt, and sugar into the blender or food processor. Process on high speed for about 1 minute. Through the lid opening, start adding the oil slowly while the blender is working. Keep blending until all of the oil is used up and the mayo is smooth and creamy.