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1
Place the unpeeled potatoes in a pot of cold salted water or set them in a steamer basket. Cook at a gentle simmer until a skewer meets no resistance at the centre. Drain immediately.
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2
While still very hot, peel the potatoes by hand, removing all skin. Return the peeled flesh to the dry pot over medium heat and stir continuously until no steam rises and the surface of the potato looks dry and slightly chalky — every trace of residual moisture must be driven off before the butter is added.
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3
Pass the hot dried potato through a fine drum sieve (tamis) directly into a clean, warm, heavy pot. Work in batches, pressing firmly with a plastic scraper; the purée beneath the tamis must be uniformly smooth and entirely free of fibre or grain.
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4
This is where the dish lives or dies. Set the pot of sieved potato over the lowest possible heat. Add the cold butter piece by piece, beating each piece fully into the purée with a stiff spatula or wooden spoon before adding the next. The potato must remain hot enough to melt each piece of butter, but the cold butter in turn moderates the temperature — if at any point the surface of the purée appears greasy or the mixture looks oily and separated, the emulsion has broken and the heat was too high. The finished mass must be glossy, cohesive, and intensely rich.
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5
Pour in the hot milk in a thin stream, beating steadily, until the purée reaches a pourable, flowing consistency that falls from the spoon in a slow, silky ribbon.
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6
Taste and adjust for salt. Pass through the tamis a second time if a finer texture is desired. Serve immediately; the purée does not hold without loss of texture.