Preheat the oven to 200 degrees. Line a rimmed baking sheet with parchment paper, and place it on the center rack of the oven. Peel the carrots, parsnips, and potato, and grate them on the large holes of a box grater. Place the grated vegetables on a clean kitchen towel, fold it around them, and squeeze tightly to remove all excess moisture. Transfer the grated vegetables to a large mixing bowl. Add the sliced scallions, flour, and salt and pepper, and toss to combine well. Add the lightly beaten eggs, and mix well.
Heat a large nonstick skillet over medium heat, and add 2 teaspoons vegetable oil. Make a few latkes at a time; for each, shape 2 tablespoons of the vegetable mixture and place in the skillet. Cook 2 minutes on each side, until golden and crisp. Transfer cooked latkes to prepared baking sheet in oven to keep warm. Repeat with remaining oil and latke mixture.
Serve the latkes warm with dollops of sour cream, and salt and pepper to taste.