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1
Place the tofu block, uncovered, in the refrigerator for 30 minutes. Cold tofu is marginally firmer and will hold its structure during cutting. The block is ready when it feels cool and slightly resistant to the gentlest press of a fingertip.
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2
Set the chilled tofu on a flat, dry board. With the sharpest, thinnest blade available, cut the block horizontally into slices of approximately 1 mm — each slice the thickness of a coin's edge. Use a single, decisive, forward-drawing stroke; slow or tentative pressure will crush rather than cut. The slices are done when they lie flat and translucent, intact at every edge.
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3
This is where the dish lives or dies. Lay each horizontal slice flat and cut downward into threads of the same 1 mm width, again with a swift, confident stroke. A single hesitant or sideways movement will shatter the thread. Work across the full slice without lifting the knife between strokes. The finished threads should be uniform, freestanding, and fine enough to tremble at the slightest disturbance.
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4
As each set of threads is cut, slide them gently — do not lift in a cluster — into a bowl of cold water. They will separate and float individually. Hold in cold water until the stock is ready; the threads are ready when they move freely without clumping.
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5
Bring the superior stock to a gentle simmer in a wide pan. If using ham or mushroom shreds, add them now and allow them to warm through. The stock should be clear and trembling at the surface — never at a rolling boil, which would break the threads on contact.
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6
Drain the tofu threads from the cold water. Ladle a portion of the hot stock into each warmed bowl, then lower the threads in by sliding them from a flat spoon or spatula just beneath the surface. They are ready when they hang suspended in the clear stock, moving with the liquid like the finest noodles. Scatter scallion greens over the surface and serve immediately.