Boil the potatoes (in their skin) until they are tender all the way through. You can test this by poking a potato with a knife or skewer and see if it slides easily all the way to the center.
Let the potatoes cool completely, peel them, and cut them into bite-size pieces.
Wash the scallions, remove outer parts that are wilted. Cut off the tip of greens and the root. Then chop the scallions.
Put all the mayonnaise ingredients into a blender or food processor and mix until you have a creamy paste similar to regular mayonnaise. Taste test and adjust with salt and pepper according to your taste.
Pour the mayonnaise over the potatoes and gently combine to not crush them.