How to Make It
Make the dashi In a large saucepan, combine all of the ingredients with 10 cups of water and bring to a boil. Reduce the heat to low and simmer until reduced to 4 cups, about 30 minutes. Strain the dashi through a fine-mesh sieve set over a medium bowl; discard the solids and wipe out the saucepan.
Make the stew In the saucepan, heat the oil. Add the mushrooms, onion, garlic, the sliced white and light green scallions and the 1/2 cup of kimchi and cook over moderate heat, stirring, until the onion is beginning to brown, about 8 minutes. Add the dashi, gochugaru, soy sauce and fish sauce and bring to a simmer. Add the shrimp and mussels, cover and cook over low heat until the mussels open, about 2 minutes. Discard any mussels that don’t open. Stir in the calamari and tofu. Carefully crack the eggs into the stew. Cover and cook until the egg whites are set but the yolks are still runny, 2 to 3 minutes.
Ladle the tofu stew into bowls and garnish with the watercress and sliced scallion greens. Serve with kimchi.