Preheat the fryer. In a mixing bowl, whisk the egg, flour, cornstarch, soda water and salt. Blend until smooth. Let the batter sit for 10 minutes to rest. Using the back of a French knife, crack the crab shell and expose the meat. In a food processor, combine all of the remaining ingredients except for the olive oil. Pulse until smooth. With the machine running, slowly add the olive oil in a steady stream. Season with salt and pepper. The mixture should be thick. Dip the exposed meat part of stone crab in the tempura batter. Fry the stone crabs for about 3 to 4 minutes, or until slightly golden brown. Remove the stone crabs from the oil and drain on a paper-lined plate Season with salt and pepper and serve with tartar sauce.