Place the kombucha, egg yolks, mustard powder, onion powder, garlic powder, and salt in the work bowl of a food processor, and pulse until mixed.
With the food processor running, very slowly drizzle the olive oil through the feed tube. This should take 4 to 5 minutes. Don't do it faster as it won't emulsify if the oil is added at a faster pace.
After all the oil is added, making sure it takes 4 to 5 minutes, the mayo should have a creamy consistency similar to store-bought mayo. It will thicken more after you place it in the fridge for a few hours.
Storage note: This mayonnaise can be stored in a tightly sealed container for up to three months in the refrigerator.