Put the cashews in your spice grinder or small food processor and whiz until powdered, about 30 to 60 seconds. (If you have a high powered blender, like the Vitamix, you can skip this step.)
Put the cashew powder, water, olive oil, lemon juice, vinegar, salt, mustard, onion powder, garlic powder, and black pepper in your blender and blend until smooth. Stir in the parsley.
Pour the dressing into an airtight container, cover, and refrigerate for at least 30 minutes to thicken and let the flavors develop. Store in the refrigerator for up to 1 week. Shake or whisk the dressing before each use.