Measure out your ingredients and set them out for 15 to 20 minutes to ensure they are all at the same room temperature.
Add the milk to a food processor and pulse for 30 seconds until the liquid begins to bubble. Add the yeast flakes, vinegar, mustard, salt, lemon juice, and maple syrup. Process for another 10 to 15 seconds to combine.
With the food processor running, slowly add ¼ cup of the vegetable oil, a little bit at a time. Continue pulsing until the mixture begins to emulsify (looks creamy).
Once the mixture looks creamy, begin to slowly add the remaining oil while processing.
Scrape down the sides of the bowl and process again to combine, up to 30 seconds.
Give your mayo a taste test. Here you can add a tiny bit more salt, nutritional yeast flakes, or maple syrup.
Transfer to a lidded glass jar and refrigerate where it will thicken even more upon being chilled. It will keep for up to 1 month in the fridge.