Meanwhile, prepare the dressing. Add all of the ingredients to a high powered blender, such as a Vitamix, starting out with JUST 3/4 cup milk process until very smooth and creamy on high. If using canned coconut milk, make sure you have shaken the can really well first. Scrape the sides a couple of times and blend again for a good couple of minutes so it gets really smooth and thickens. The dressing will be fairly thin, but will thicken well in the fridge. Add more milk if you want it thinner.
Pour into a container and chill in the fridge for an hour or two to marinate, so it gets cold and thickens further. The flavor really is best after it chills and marinates (even better overnight!). If you like, chill the potatoes as well. (I chilled both the dressing and potatoes overnight) When ready, remove the dressing and stir well. Toss the potatoes with as much dressing as you like. (There will be leftover dressing) Taste and add any extra salt for flavor and garnish with more dill and fresh chopped parsley, if desired. The extra dill and parsley really adds a nice flavor and presentation.