Preheat oven to 250°F (121°C). Place a wire rack on a rimmed baking sheet.
Place whisked eggs in a bowl. Season with salt and pepper.
Grate potatoes, parsnips, and onion with a food processor or box grater.
Add grated vegetables and bread crumbs to eggs and toss to combine.
Heat 3 tablespoons of oil in a large skillet over medium heat. Drop about 1/4-cup spoonfuls of potato mixture into skillet; flatten to create even pancakes. Cook, turning once until browned (approximately 8 to 12 minutes in total). Transfer the cooked latkes to the prepared baking sheet and keep warm in the oven.
Repeat Steps 1-5 with the remaining potato mixture, adding more oil to the skillet as needed (when getting near the end of the potato mixture, strain, and discard any liquid at bottom of the bowl).
Optional: Serve with sour cream and applesauce for dipping.
Notes:
Quick Tip
Reduce your cooking time by using two frying pans instead of one!