Bring 4 quarts of water to a boil and add 2 tablespoons salt. Cook the celery in the boiling water for 7 minutes, until tender but not soft. Drain and set aside on paper towels to cool.
In a heavy-bottomed skillet, heat the oil until it is almost smoking. While the oil heats, place the flour on a plate and place the eggs in a shallow bowl. Dredge the cooled celery pieces through the flour, then the egg and cook them in the oil until they are deep golden brown. Remove with a slotted spoon to a plate lined with paper towels. Season with salt and pepper and serve.