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1
Place the jointed hen, halved onion, carrot, celery stalk, celery root, Chinese celery, and dried yellow chillies in a large pot. Cover with cold water — the cold start is essential to a clear broth. Bring slowly to a bare simmer. The surface will show a grey foam; skim it continuously until it subsides and the liquid runs clear.
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2
Maintain the barest possible simmer — the surface should tremble, not boil — for a minimum of two hours. This is where the dish lives or dies: a rolling boil will cloud the stock and deny the collagen the low, sustained heat it requires to dissolve; an impatient cook pulling the hen before two hours will find the muscle fibres still resistant and the broth thin. The hen is ready when the meat yields completely to the pressure of a spoon and the broth has body without any reduction.
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3
Lift the hen pieces from the broth. Strain the stock through a fine sieve, discarding the spent aromatics. Return the strained broth to a clean pot and bring it back to a simmer. Season with salt.
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4
Add the potato halves to the simmering broth and cook until a skewer passes through without resistance. Add the egg noodles and cook until just tender. The broth should remain clear and trembling throughout.
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5
Pull the hen meat from the bone in large pieces and divide it among warmed bowls. Ladle the broth over, distributing noodles and a piece of potato into each bowl. Set one soft-boiled egg into each bowl at the moment of service. Its yolk, broken by the diner's spoon, enriches the broth with fat and protein in the bowl itself.