Rinse dried black jujubes under running water; Put them in a bowl; Fill the bowl with water; Add 1 tsp salt into the water; Leave it for 15 minutes; Remove them; Rinse them under running water again; Drain them.
Rinse and drain dried bastarg ginseng root.
Rinse, drain and slice ginger.
Rinse pumpkin under running water; Drain it; Slice off the stem; Cut the pumpkin in half with a cleaver; Scrape out the seeds; Peel it with a vegetable knife; Cut it into chunks.
Fill a deep plate with water; Stir 2 tsp salt into the water; Carefully put tofu into the plate; Leave it for 30 minutes; Carefully discard the water; Cut the tofu into pieces.
Hold carp firmly by the head and scrape the scales from the tail towards the gills with a fish scaler; Rinse the fish under running water; Insert the knife into the anus near the tail; Draw the knife toward the head, splitting the fish to the base of the gills; Spread the abdominal cavity with fingers; Reach in and pull out the entrails; Rinse the cavity under running water; Cut off the head with the knife; Rinse the fish under running water again; Pat-dry the fish with kitchen paper.
Add 1 tbsp oil to a non-stick pan; Add the ginger and stir-fry it over a high heat till fragrant; Turn to a low heat; Arrange the fish into the pan; Turn to a high heat; Pan-fry the fish over a high heat till both sides are slightly brown; Turn off the heat; Gently pat-dry the fish with kitchen paper.
Fill a pot with 2.5L water; Bring to the boil over a high heat; Add the papaya, the tomatoes and the tofu skin and bring to the boil over a high heat again; Turn to a low heat; Cover the pot with its lid; Cook over a low heat for 1.5 hours; Add the fish and the tofu, and bring to the boil over a high heat again; Turn to a medium heat; Cook over a medium heat for 20 minutes; Stir seasonings into the soup; Turn off the heat; Arrange the soup into serving bowls; Read to serve.