Combine milk and ground flax in a blender. Blend on high speed until flax meal is barely noticeable, and the mixture is frothy, about a minute.
Add the sugar, dry mustard, onion powder, salt, vinegar and lemon juice, blending for a few seconds to combine.
Now begin to add the oil. With the blender running, use the hole at the top to stream in a tablespoon at a time, blending for about 30 seconds after each addition.
Give your blender a break every now and again so that it doesn’t heat up the mayo. You should notice it thickening by the halfway point.
By the time you’ve used ¾ of the oil, it should be spreadable. And with the last addition, you should have a thick mayo. If it seems watery, keep blending.
Transfer to glass tupperware, seal tightly and refrigerate for a few hours, and it will thicken even further. Use within a week.
