Shell the large cooked prawns, refrigerate the meat, and reserve the heads and shells to create a deeply flavorful broth. Peel and finely chop the onions. Peel and crush the garlic cloves.
Heat the sunflower oil in a large casserole over high heat. Brown the prawn heads and shells with the onions and garlic. Add the dried lemongrass, powdered ginger, chili powder, salt, and pepper. Pour in 1.25 liters of water and the fish stock. Stir well and simmer gently for 30 minutes. Strain the broth, taste, and adjust seasoning if needed.
Squeeze the lemon to extract the juice. Peel the carrots and slice into thin strips with a peeler (julienne). Clean the shiitake mushrooms and slice thinly. Bring the fragrant broth to a boil, add the carrots, and cook for 5 minutes. Add the prawns and mushrooms at the end, just to warm through—the mushrooms should stay crunchy.
Serve steaming hot in bowls. Drizzle with lemon juice, sprinkle with chopped coriander, and add nuoc mam drops to taste.
