Soak the dried shitake mushrooms in 1/2 cup of warm water for half an hour. Remove the mushrooms and chop them. Reserve the water to make the stock.
In a food processor (or by hand) finely mash the tofu into a fine paste
Chop the fresh mushrooms, carrots, cilantro and green onion. Mince the raw, shelled and deveined prawns and mince them.
Mix the mashed tofu with the minced prawns, chopped mushrooms, carrots, cilantro, green onion, egg white, salt and pepper, potato flour. Mix well till smooth and well blended.
Scoop a tablespoonful and place on a chinese spoon used as a mould to form the pipa shape. Repeat with remaining mixture. Place the tofu balls in a lightly oiled microwave safe plate.
Microwave the tofu balls for 2 minutes. Remove and let cool. When cool, dust each tofu ball with all-purpose flour.
In the meantime, in a medium sauce pan, heat the oil till very hot (350 F or 175 C), deep fry the tofu till just golden (the crust should be crispy with a soft center), about 2 minutes, swirl the tofu so all sides are evenly golden. Remove and drain on a plate lined with kitchen paper towel.
Instead of deep frying, the tofu can also be air fried. Preheat the air frier to 400F / 200 C. Gently spray each tofu morsel with oil (or lightly coat each tofu piece in oil with a pastry brush). Air fry for around 4 to 5 minutes, turn over and air fry for another 3 to 4 minutes till golden on both sides.
To make the sauce: In a frying pan, heat 1 tablespoon of oil, stir fry the ginger, sliced shitake mushrooms. Add the Chinese vegetables till just wilted. Add the light and dark soy sauce, Chinese wine or sherry, the vegetable stock or dry shitake soaking water and heat through.
Mix the potato flour with a little water to make a slurry. Gradually add to the pan to thicken the sauce to the desired consistency (you may not need the full slurry amount).
To serve, display the Chinese vegetables around the plate, put the pipa tofu in the center, and spoon the sauce over the tofu, and drizzle the sesame oil. Sprinkle the sliced scallion on top and serve hot with steamed rice.