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1
Combine the soy sauce, gochugaru, sugar, garlic, and ginger in a bowl and stir until the sugar dissolves. Taste the sauce before it meets the chicken — it must be assertively seasoned, saltier and spicier than the finished dish will be, because once the noodles go in they will drink up every drop of this liquid and carry it to the centre of the braise. Adjust before proceeding.
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2
Place the chicken pieces in a wide, heavy braising pot or deep sauté pan, pour over the sauce and the water, and bring to the boil over high heat, then reduce to a steady simmer. Braise uncovered for 20 minutes, turning the chicken once, so that the exposed side colours and the sauce reduces and darkens rather than simply steaming the meat. The flesh should be just cooked through and the sauce visibly deepened in colour by the end.
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3
Add the potatoes, carrot, and onion and continue braising for a further 10 minutes, so the vegetables cook in the seasoned braising liquid and take on its colour and depth rather than tasting of plain starch. The potato should yield to the tip of a knife without resistance before you move on.
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4
This is where the dish lives or dies. Check that sufficient liquid remains in the pot — there must be enough to hydrate the noodles completely without the pot running dry and the dangmyeon scorching on the bottom — then add the soaked, drained dangmyeon and press them gently under the liquid. Braise for 10 minutes, turning the noodles periodically, until they are fully translucent, glossy, and coated throughout with the concentrated braising liquid, having absorbed most of the sauce.
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5
Scatter the spring onions over the surface and remove from the heat. Rest for 2 minutes, so the residual heat finishes the noodles at the centre without overcooking them in the pot. The noodles should be yielding but with slight resilience at the centre; the sauce should be almost entirely absorbed, coating every strand.