How to Make It
Preheat oven to 300°F. Set a wire rack in a rimmed baking sheet. Grate carrots, parsnips, and beet on the largest holes of a box grater. Grate onion to measure ⅓ cup (reserve remaining onion for another use). Stir grated vegetables, cornstarch, scallions, eggs, and 1 teaspoon salt in a large bowl until fully combined. (Do not let sit; mixture will become watery.)
Heat 1 tablespoon oil in a large non-stick skillet over medium. Drop latke mixture into hot skillet by ⅓ cupfuls to form 4 patties, pressing gently with a spatula to even out tops. Cook, flipping once, until latkes are golden brown, about 4 minutes per side. Transfer to baking sheet and place in oven to keep warm. Repeat with remaining oil and latke mixture.
Season cooked latkes with 1 teaspoon salt right after frying. Stir together yogurt, dill, pepper, and remaining ¼ teaspoon salt in a small bowl. Serve yogurt sauce with latkes.