Place the potatoes in a large pot and cover with cold water. You can add some salt here, if desired. Bring to a boil, then reduce the heat and simmer, uncovered, until fork-tender, about 10 minutes. Careful not to overcook as they will fall apart if too tender.
Drain then transfer to a large bowl to cool.
In the body of a food processor or blender, add all the dressing ingredients.
Blend until well combined and smooth.
Add the celery, shallot, green onions, hard boiled eggs, and fresh herbs to the cooled potatoes.
Pour the creamy dressing over top.
Stir to combine. Add more salt and pepper, if desired. Serve cold.