Use the yolk from an intact shell that has been heat-treated in a 135 F/57.2 C circulating-water bath for a full 75 minutes after the bath has recovered to 135 F, then thoroughly chilled. Separate the yolk.
In a narrow straight sided vessel, combine the yolk, distilled vinegar, apple cider vinegar, water, salt, and sweet paprika. Pour all the soybean oil over the aqueous mixture. Let the layers settle for 5 minutes so the water-rich phase remains beneath the oil.
Set the immersion blender head flat on the bottom of the vessel. Blend at high speed without lifting until a thick, pale emulsion is established around the head.
Raise the blender slowly through the remaining oil until fully incorporated. Stop as soon as the mayonnaise is smooth and uniform.
Seal tightly with a lid and refrigerate promptly.