Preheat the oven to 400°. Working over a large bowl, coarsely shred the celery root and potato on the large holes of a box grater. Using 2 forks, toss the celery root and potato with the onion and salt.
In a large nonstick skillet, heat 1 1/2 tablespoons of the oil. Scoop four 1/2-cup mounds of the vegetable mixture in the skillet and flatten into cakes. Cook the pancakes over moderately high heat until browned and crisp, about 4 minutes per side. Transfer to a large baking sheet and season with pepper; keep warm in the oven. Repeat with the remaining oil and vegetable mixture. Serve the pancakes hot.
The fried pancakes can be refrigerated overnight. Bring to room temperature before reheating in a 375° oven.