In a large liquid measuring pitcher, add chickpea brine, vinegar, lemon, mustard, garlic, sugar and salt. Using an immersion blender, mix until combined. While the blender is running, very slowly add the oil (doing so in a thin stream). It should take several minutes to add the complete amount of oil to the mixture. Keep blending until the mixture emulsifies and thickens.
Notes
Tip #1: If you have time to reduce the chickpea brine on the stove by 25%, the juice will be a lot more gelatinous and make the mayo creamier.Tip #2: Will not work in a food processor.Tip #3: Store in refrigerator for up to 5 days.