Place the body of the crab on its back and remove the central body part (the piece where the legs were attached) from the shell. Using a chopstick, remove any white meat from the leg joints and add to the claw and leg crabmeat. With a spoon, scoop out the soft brown meat only and add to the bowl, then remove all remaining parts from inside the shell and discard. Rinse out the shell with water and drain.
Add the smelt roe to the crabmeat and season with salt and pepper. Add a layer of the mixed crabmeat to the shell, covering the whole cavity inside and then place a layer of sea urchin on top. Cover the sea urchin with a layer of mushrooms, then do the same with the green onion and finally the Parmesan cheese.
Beat the egg whites in a clean bowl until they form stiff peaks, then cover all of the filling inside the crab shell with the beaten egg whites and smooth over the top with a metal spatula.
Bring about 1 and 3/4 inches of oil in a shallow pan to 325°. Slip the shell carefully into the oil, egged side up and cook for 10 minutes, until the beaten egg white puffs up. Carefully remove and place on a suitable serving dish.
Dress with the seaweed and serve immediately.
Notes: During cooking, make sure the height of the oil is no more than the height of the shell. The oil should not be so high that it gets inside the shell from the top.
By the time the egg whites begin to froth and cook, the crab filling inside will be thoroughly heated through.
*Masago: This is the roe of the smelt fish, which is often used as a sushi topping and garnish.