Add the frying oil to a small pot and heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F. When hot, add the celery root to the oil and fry until golden brown. Drain from the oil.
Place the burger patty on a flattop or in a skillet set over medium heat. Cook for 2 minutes on each side for medium doneness. Place the hot sauce and blue cheese on the burger, and then cover with a steam dome or the lid for the skillet.
Split the hamburger roll open and butter each side. Toast the bun split-side down on the flattop or in a separate skillet set over medium heat.
To finish, place the burger patty on the bottom half of the bun, top with the fried celery root, and then serve.