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.