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1
Melt the butter in a heavy saucepan over low heat. Add the sliced leeks — white and very pale green only. Soften without colour for 15 minutes, stirring occasionally, until completely soft and translucent. The leeks must show no trace of browning.
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2
Add the diced floury potato, the light chicken stock, and salt. Bring to a gentle simmer. Cook for 20 minutes, until the potatoes are completely tender and offer no resistance when pressed against the side of the pan.
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3
Transfer in batches to a blender — not a food processor — and process to a fine, smooth purée. Pass the entire batch through a fine drum sieve. Any grain or texture variation remaining at this stage cannot be corrected later.
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4
Return the sieved soup to a clean pan. Add the first measure of heavy cream and stir to combine. Assess consistency: the soup should flow from a ladle as a thin, smooth, even ribbon. If too thick, add cold cream in tablespoon quantities and recheck.
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5
Transfer the soup to a bowl set over a larger bowl of ice. Stir regularly until the soup is completely cold. Add the second measure of cold heavy cream to adjust the final consistency and lower the base temperature further.
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6
Season the soup only when it is fully cold — this is the decisive step on which the dish lives or dies. Cold suppresses salt perception consistently; the finished soup requires approximately 25% more salt and white pepper than the same soup would need at serving temperature. Taste and correct until the soup reads clean, slightly sweet from the leek, smooth from the cream and potato, and properly salt-forward. A soup seasoned hot and not corrected cold will taste flat at table.
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7
Ladle into chilled bowls. Garnish with a small quantity of precisely cut chives. Serve immediately.