Sujebi Kimchi Soup

Mix 1⅔ cups (208 g; or more) all-purpose flour, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and 2 tsp. vegetable oil in a large bowl. Gradually drizzle in ⅓ cup plus 1 Tbsp. (104 g) water, mixing with your hand like a claw until dough comes together and forms a ball (it will be shaggy and sticky; but don’t worry, it will get smoother when you knead it). If dough feels too dry, add more water, 1 Tbsp. at a time; if it feels too wet, add more flour, 1 Tbsp. at a time. Knead dough until it pulls away from the sides of the bowl and is taut with a smooth skin, 8–10 minutes. Wrap dough in plastic or place in a resealable plastic bag and close. Let rest at room temperature while you prepare the soup (at least 15 minutes). Do ahead: Dough can be made 12 hours ahead. Chill. Bring to room temperature before using.

Heat 2 tsp. vegetable oil in a medium Dutch oven or other heavy pot over medium heat. Add 8 oz. ground beef or pork and sprinkle with ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt. Spread meat out in an even layer and cook, undisturbed, until a light crust forms underneath, about 1 minute. Using a flat-edged wooden spoon or heatproof rubber spatula, break up meat and continue to cook, stirring and breaking up as much as possible, until brown all of the way through, about 2 minutes more. Add 1 small onion, coarsely chopped, and 5 garlic cloves, coarsely chopped, and cook, stirring, until combined and fragrant, 30–60 seconds. Mix in 2½ cups drained ripe kimchi (about 1 lb.), chopped into bite-size pieces  (along with any clinging juices), then 1 (heaping) Tbsp. gochujang (Korean hot pepper paste). Pour in 7 cups cold water and stir well. Increase heat to medium-high and bring to a boil. Reduce heat to medium-low, cover pot partially with a lid, and simmer, decreasing heat to low if needed, until kimchi is softened, 15–20 minutes. (If soup has reduced too much, add up to another 1 cup water and return to a simmer over medium-low heat.)

Add 1 Tbsp. fish sauce, 1 Tbsp. soy sauce, and remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt to soup. Taste and add more gochujang and/or season with more salt if needed.

Unwrap dough and divide into 2 or 3 manageable pieces. Hold 1 piece of dough in your hand and stretch off a small piece with your other hand until thin and 1"–2"-long (the thickness doesn’t need to be perfectly consistent). Tear piece off and lay gently in simmering soup (still over medium-low). Continue with remaining dough, working as quickly as you can. Give sujebi a gentle stir and cook, stirring occasionally, until cooked through (if you try one, there should be no floury taste) , about 5 minutes. Taste sujebi and season with more salt if needed. Remove from heat; drizzle in ¼ tsp. toasted sesame oil and top with three fourths of 2 scallions, chopped.

Ladle sujebi into bowls and top with remaining scallions.