How to Make It
In a large pot, heat the oil. Add the scallions and cook over moderate heat until softened, 2 minutes. With a slotted spoon, transfer the scallions to a plate. Add the onion and garlic to the pot and cook, stirring occasionally, until softened, 7 minutes. Add the daikon and kimchi and cook for 1 minute. Add the water and bring to a boil.
Add the lobster to the pot and simmer over moderate heat, turning, until the shells are bright red, 6 minutes. Transfer the lobster to a large rimmed baking sheet. When cool enough to handle, remove the tail and claw meat; discard the dark intestinal vein that runs down the tail. Cut the meat into bite-size pieces. Discard the tail and claw shells. Return the lobster body to the pot. Cover and simmer over low heat for 10 minutes. Discard the lobster body shells.
Stir the fish sauce, soy sauce and red pepper paste into the broth and bring to a boil over moderately high heat. Add the clams, cover and cook until they are all open. Add the lobster meat, scallions and watercress to the soup and remove from the heat. Ladle into bowls and serve.
The recipe can be prepared through Step 2. Refrigerate the lobster and broth separately overnight.
The easiest way to split live lobsters open is to ask your fishmonger to do it; he can also remove the claws and tails.