Add the quartered potatoes to a large pot and cover them completely with water by 1 or 2 inches. Place a lid on the pot at an angle and simmer over medium heat for 20-25 minutes, or until you can pierce them with a fork.
Drain the potatoes and set them aside to cool.
Make the dressing by draining and rinsing the cashews and placing them into the blender, along with the rest of the "dressing" ingredients (dates - make sure to drain the water and remove the pit before adding the dates to the blender - garlic, mustard, nutritional yeast, apple cider vinegar, salt and water). Blend until totally creamy and smooth, about a minute. Set aside for now.
When the potatoes are cool enough to handle, cut them into bite-sized pieces and place them into a large mixing bowl, along with the celery, onion, parsley, dill, and all of the Dressing that you just made.
Gently stir until everything is combined and add salt and pepper to taste. Chill for at least an hour before you devour.