Add remaining ingredients except parsley, dill, chives, and dried minced onion in blender. Blend until very smooth and creamy.
Scrape down sides of blender, replace lid, and blend again. A heavy-duty blender works best to get the sunflower seeds smooth and creamy. Other blenders tend to leave a little bit of graininess in the dressing.
Add remaining ingredients and pulse just until mixed.Chill before serving. (This will thicken slightly in the frig.) Keeps in the frig for about 5 days.