Prepare the vegetables as noted above and place them in a large bowl. Toss with 1/2 teaspoon salt and fresh ground black pepper.
Make the dressing: Place all ingredients in a food processor, smaller blender or the cup of an immersion blender (also works in a standard blender). Blend to combine. Taste and add another pinch of salt if necessary.
Add the dressing and toss with the salad, adding Parmesan shavings to garnish if using. Taste add additional salt if desired. Eat immediately. If making in advance, leave the dressing separate from the vegetables until serving.