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1
Combine the flour (and potato starch if using), water, and salt in a bowl, working the mixture until a rough mass forms, then knead on a clean surface for 8–10 minutes until the dough is very smooth and no dry flour remains. Wrap tightly and rest at room temperature for a minimum of 30 minutes, so the gluten strands relax fully and the dough becomes extensible enough to tear thinly without snapping back. The dough is ready when a small piece tears cleanly and does not spring back toward its original shape.
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2
Place the dried anchovies and dashima in the water and bring to a brisk boil, then simmer for 15 minutes — keeping the heat at a steady simmer rather than a hard boil so the dashima has no chance to turn the broth bitter and cloudy. Remove and discard both solids. The broth should smell clean and savoury, of the sea without fishiness.
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3
Add the potato chunks to the broth and cook over medium heat until just yielding at the edge when pressed with a spoon, about 10 minutes; starting the potato before the courgette ensures both vegetables arrive at the table with the right texture and neither is sacrificed for the other. Add the courgette and cook for a further 3 minutes until bright and beginning to soften.
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4
Raise the heat to bring the broth to a full, rolling boil. This is where the dish lives or dies: the broth must be at a vigorous boil before a single piece of dough enters the pot, so the fierce heat sets the shape of each piece the moment it hits the liquid and the pieces cannot sink, fuse together, or glue themselves to the base. Take the rested dough ball in one hand and, working directly over the pot, tear pieces roughly the size of a large postage stamp — approximately 2–3 mm thick at the centre — dropping each piece immediately into the boiling broth.
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5
Stir once, gently, to ensure no pieces have adhered to the base of the pot, and cook for 5–7 minutes, stirring only occasionally and with care so the pieces keep their torn shape rather than breaking into ragged shreds. The dough pieces are done when they turn translucent and rise to the surface; the broth will have thickened slightly from the dough starch.
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6
Ladle into deep bowls, distributing dough pieces, vegetables, and broth evenly. Serve immediately with a side of kimchi, bearing in mind that the broth will continue to thicken as the meal progresses.