On a mandolin shave raw cauliflower and transfer to a bowl. Shave red onion and add to the bowl with the cauliflower. Shave radish on mandolin and julienne with a knife add to bowl as well. Pick parsley leaves and add to the salad. Add baby arugula and set aside.
In a medium bowl, add all the ingredients to and mix until all combined. Should be the consistency of thin ranch. If its too thick, add a couple tbs of water.
Add a couple tablespoons of dressing at a time and lightly toss it until the cauliflower and arugula have a light shine of dressing. Finish by shaving parmesan over the top and drizzle with olive oil. Season with salt and pepper.