Make the dough with a food processor: Pour ¾ cup water into the bowl, then add the salt, oil, and flour. Process for about 1 to 2 minutes until the dough forms into a ball. Transfer the dough into a plastic bag and knead for another minute through the bag. Set aside to rest.

…or make the dough by hand: Combine the flour, kosher salt, oil, and ¾ cup water in a large bowl. Mix with a wooden spoon until the ingredients come together into a lumpy dough. Knead the dough by hand for 10 to 12 minutes, until it forms a smooth ball. Seal in a plastic bag and set aside to rest.

Make the soup: Put the cleaned anchovies into a soup pouch and seal it tightly. In a large pot, combine the water, anchovy pouch, kimchi, kimchi brine, onion, and garlic. Cook for 25 minutes over medium high until the kimchi turns a little soft and the broth is nicely infused with the anchovy flavor. Take out the anchovy pouch and discard. Add the fish sauce (or salt to your taste).

Make the noodles and serve: Take the dough out of the plastic bag. Knead it on a cutting board or just in your hands for 1 to 2 minutes until it’s soft and smooth. Uncover the soup and bring it back to a boil. Divide the dough ball into 2 pieces. Hold a dough ball in one hand and with your other hand pull the dough and stretch out a little bit until you get a paper-thin, bite-size piece. Tear it off and drop it into the boiling soup. Repeat until all the dough is used up. Stir the noodle soup with a ladle or wooden spoon. Add the gochujang, green onions, cover, and cook for 5 minutes until all the noodles are floating and cooked through. Remove from the heat and stir in the toasted sesame oil (if used). Ladle the soup into individual bowls and serve right away.