Add aquafaba to a tall glass jar along with ground mustard, sea salt, apple cider vinegar, and brown rice syrup. Blend on high with an immersion blender for best results (we haven't had good success with traditional blenders).
Measure the oil in a liquid measuring cup that has a spout. Then, with the immersion blender on its highest speed, begin slowly dripping in the oil. Increase the drips to a very small stream (about the width of a toothpick), adding the oil very slowly over the course of 1-2 minutes (we recommend setting a timer to help pace it). Adding slowly supports the immersion process.
Move the immersion blender up and down to incorporate a little air toward the end. If it's looking too thin, add more oil. The more oil you add, the creamier, thicker, and denser the texture will become. You shouldn't need more than the recommended amount.
Taste and adjust flavor as needed, adding more sweetener of choice for sweetness (keeping in mind maple syrup will make it less thick + fluffy), vinegar for tanginess, salt for saltiness, or ground mustard for mustard flavor. I added a bit more of each.
Use immediately or transfer to a sealed container in the refrigerator until cold - about 4 hours. It will thicken even more in the fridge! Store leftovers in the refrigerator up to 2 weeks (sometimes longer). You'll know it's gone bad when mold has formed. Not freezer friendly. Perfect for sandwiches, dressings, sauces, and more!