How to Make It
Grate potatoes, carrots, parsnips, and onion in a food processor fitted with a large shredding blade. Transfer mixture to a clean dish towel, and squeeze well to remove excess liquid; discard liquid. Transfer potato mixture to a large bowl. Add flour, egg, salt, pepper, and baking powder; stir well.
Preheat oven to 200°F. Pour oil to a depth of about 1/3 inch in a large skillet; heat over medium-high. Working in batches, drop spoonfuls (about 2 1/2 tablespoons each) of batter into skillet, leaving 2 inches between. Using back of spoon, gently flatten batter into disks. Cook, flipping once, until golden brown and crisp, 4 to 5 minutes. Place fritters on a plate lined with paper towels to drain. Transfer fritters to a wire rack set in a rimmed baking sheet, and keep warm in preheated oven while frying remaining batches.
Arrange fritters on a serving platter; top evenly with sour cream and dill. Sprinkle with black pepper.