Preheat oven to 425 degrees F. Line an extra-large baking sheet with parchment paper; coat parchment with cooking spray. In a medium bowl whisk together egg, flour, salt, and pepper.
Peel and finely shred potatoes. Press shredded potatoes between several layers of paper towels to remove any excess moisture. In a large bowl combine shredded potatoes, zucchini, and carrots. Add egg mixture; stir just until combined.
Drop potato mixture by rounded tablespoons onto the prepared baking sheet. Using the back of a spoon, flatten mounds slightly. Coat mounds with cooking spray. Bake 7 minutes. Turn pancakes; bake about 7 minutes more or until lightly browned.
Meanwhile, for herbed creme, combine yogurt, basil, and chives. Serve with warm potato pancakes.