For the noodles: Mix together the flour, sesame oil, egg, 1 teaspoon salt and 1/3 cup warm water in a large bowl. Knead until a dough forms, about 10 minutes. Cover with plastic wrap and refrigerate for at least 1 hour and up to overnight.
For the sauce: Combine the soy sauce, fish sauce, gochugaru, sesame seeds, sesame oil, ginger, garlic and scallions in a small bowl. Whisk to combine, cover with plastic wrap and set aside for at least 1 hour.
Roll out the dough using a rolling pin until it is 1/8 to 1/16 inch thick. Starting at one end, roll the dough into a cylinder, then use a sharp knife to cut it into 1/8-inch-thick noodles. Put the noodles on a parchment-lined baking sheet sprinkled with additional flour, making sure that you use your fingers to separate the noodles so they do not stick together; set aside.
For the broth: Put the dried anchovies, dried shrimp, garlic, mushrooms, kombu, daikon, onion and 3 quarts water in a medium saucepan. Bring to a boil over medium-high heat, then reduce to a simmer and cook for 20 to 30 minutes. Strain into another medium saucepan and discard the solids.
For the seafood and toppings: Bring the broth back to a boil and add the seafood. Cover with a lid and cook until the shellfish is open and the shrimp is just cooked through, about 5 minutes. Remove the cooked seafood to a medium bowl and reserve.
Add the cut noodles and zucchini to the broth and cook until the noodles are just tender, a few minutes. Stir in the eggs and 2 teaspoons salt. Remove from the heat and divide among 4 bowls. Top evenly with the seafood, drizzle with half the sauce and garnish with sliced scallions and some black pepper. Serve immediately with the remaining sauce on the side.
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