Heat oil in a large nonstick saucepan over medium heat.
Add lemongrass, lime leaves, ginger, shallot, and garlic and cook until they become fragrant and soft, about 3 minutes.
Add tomato paste, shellfish stock, coconut milk, fish sauce, and palm sugar and bring to a boil. Simmer for 10 minutes.
Put the prawns in the pan and cook for 2 minutes.
Add the mussels and clams and cook for 3 minutes with the pan covered and until the shellfish have opened. Discard any clams and mussels that didn't open.
Taste the broth and and adjust with additional fish sauce, sugar, or stock to your taste.
Transfer the seafood to serving bowls, ladle the soup in the bowl, garnish with cilantro and serve immediately.