2. Refill the saucepan with water and bring it to a boil.
3. In a skillet, melt the butter and cook the onion, stirring often, for 8 minutes or until it softens. Transfer to the food processor.
4. Work the celery root and onion until mashed. Add the cream, salt, and pepper to taste. Process until smooth. Taste and add more salt and pepper if necessary. Transfer to a bowl, cover, and keep warm.
5. Place 4 eggs in the boiling water. Cook for 5 1/2 minutes. When they are done, drain them and transfer to a bowl of ice water. Very gently peel the eggs. One at a time, roll the eggs in the flour, then the egg/oil mixture, then the bread crumbs.
6. In a saucepan, heat the 3 cups of vegetable oil until hot. Gently lower the eggs into the oil and cook for about 1 minute, until they turn golden brown. Using a slotted spoon, transfer them to a plate lined with a paper towel.
7. Divide the celery root among 4 plates. Place an egg on each. Sprinkle with salt and pepper. Adapted from Neva