Put all your ingredients into the cup that came with your immersion blender, or a jar that just fits the blender head. You need a narrow container because this will help the emulsion process. Do not try to do this in a mixing bowl.
Start with the mixer head at the bottom of the jar and turn it on. Let it mix for a few seconds to start the emulsion process, then slowly lift and swirl it around the jar until the mayonnaise is thick. This will only take seconds.
Refrigerate your mayonnaise in an airtight container and plan to use within 10 days or so. The mayonnaise will thicken further as it chills.