Add aquafaba to a tall glass jar (or, if using a Magic Bullet or something similar, add to a small blender jar) along with ground mustard, sea salt, apple cider vinegar, and brown rice syrup. Blend on high with an immersion blender (or mix on your blender base) for 30 seconds until frothy.
Measure the oil in a liquid measuring cup. Then, with the immersion blender on its highest speed, slowly stream the oil in over the course of 1-2 minutes. Doing so supports the immersion process. (If using a Magic Bullet or something similar, add all the oil at once and blend on high until a thick, creamy sauce is achieved - up to 4-5 minutes, scraping down sides and shaking as needed.)
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 for 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.

1/4 cup aquafaba (the liquid/brine in a can of cooked chickpeas)
1/4 teaspoon ground mustard
1/4 teaspoon sea salt
1 1/2 teaspoon apple cider vinegar
1 tablespoon brown rice syrup (or sub stevia to taste, cane sugar or maple syrup)
3/4-1 cup sunflower oil (a neutral oil is important here for flavor, avocado or canola oil also work well)