Boil the potatoes (in their skins) until they are tender all the way through. You can test this by poking a potato with a knife or skewer and seeing if it slides easily to the center.
Let the potatoes cool completely, then peel them and cut them into bite-size pieces.
Wash the scallions and remove any wilted outer parts. Cut off the tip of the 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 and adjust with salt and pepper to your liking. Alternatively, you can use an immersion blender.
Pour the avocado mayonnaise over the potatoes and gently combine to avoid crushing them.