1. Heat the oven to 300 degrees.
2. Cut the carrot into chucks about as long as the Jerusalem artichokes. Using a mandoline or the second-largest holes on a 4-sided grater, finely shred the carrot lengthwise into a mixing bowl. Grate or mince the shallot and add to the bowl. Add the parsley, Tabasco, flour and eggs and mix well. Season with salt and pepper and mix again.
3. Just before you are ready to cook, grate the Jerusalem artichokes into the bowl and mix again.
4. Measure 2 tbls of the oil into a large heavy skillet. Heat over medium heat until a bit of the batter sizzles when dropped into the pan. Using a soupspoon, scoop out 4 mounds of the mixture into the hot oil, flattening slightly. Fry for 3-4 minutes on each side, until the pancakes are crisp and brown outside but soft inside.
5. Transfer the cooked pancakes to an ovenproof plate lined with paper towel. Keep them warm in the oven. Repeat with the remaining batter, adding additional peanut oil as necessary between each batch. Serve hot.