Combine the flour, water, and salt in a bowl. Mix until it forms a shaggy dough, then knead by hand for 5 minutes until smooth. Knead in the sesame oil if using.
Cover the dough and let it rest at room temperature for at least 20 minutes, up to an hour. This step isn't optional — unrested dough tears thick and chewy instead of thin and silky.
Meanwhile, simmer the dried anchovies and kelp in 900 ml water for 10 minutes over medium heat. Remove the kelp after 5 minutes so it doesn't turn bitter, then strain out the anchovies once the stock is done.
Bring the strained stock back to a boil. Add the onion and potato and simmer 5 minutes, until the potato is nearly tender.
Pull off a small piece of the rested dough and stretch it between your fingers into a thin, uneven sheet, roughly 3 to 5 cm / 1 to 2 in across, then drop it straight into the boiling broth. Repeat until all the dough is used, stirring occasionally so the pieces don't stick together.
Simmer 6 to 8 minutes, until the dough pieces float and turn slightly translucent at the thin edges.
Add the zucchini and garlic and cook 2 to 3 more minutes, until the zucchini is just tender.
Season with soup soy sauce, taste, and adjust with salt. Ladle into bowls, top with scallion, and serve with a small side of kimchi.