Wipe-clean tofu skin with damp kitchen paper; Tear it into few pieces.
Rinse, drain, peel and slice ginger.
Rinse papaya and pat-dry; Trim a bit off each base; Cut the papaya into halves; Scoop out the seeds; Peel; Slice the remaining.
Rinse and drain tomatoes; Tweeze off any stems; Cut the tomatoes into quarters.
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.
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 45 minutes.
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; Transfer the fish together with the ginger into the soup from the step 6; Turn to a medium heat; Cook over a medium heat for 10 minutes; Turn to a low heat; Cover the pot with its lid again; Cook over a low heat for 30 minutes; Stir seasonings into the soup; Turn off the heat; Arrange the soup in serving bowls; Ready to serve.