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1
Melt the butter in a heavy saucepan over a moderate heat. Add the flour and stir continuously with a wooden spoon for 2–3 minutes, keeping the heat low enough that the roux remains white and takes on no colour whatsoever. The roux is ready when it smells faintly of cooked pastry and no raw-flour smell lingers.
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2
Add the hot white stock in stages — a ladleful at a time — whisking the mixture smooth after each addition before introducing the next. Once all the stock is incorporated, the liquid should be fluid and lump-free. Bring to a gentle simmer.
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3
Maintain a slow, steady simmer for 45–60 minutes. Skim the surface at regular intervals, removing the grey scum of coagulated proteins that rises as the sauce heats. This is where the dish lives or dies: insufficient simmering leaves a persistent flour taste and a muddy, impure flavour; patient skimming over the full duration refines both the flavour and the clarity of the sauce. A cartouche may be laid on the surface between skimmings to prevent a skin from forming. The sauce is ready when it tastes cleanly and unmistakably of its stock — of chicken, veal, or fish — with no trace of raw flour.
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4
Pass the finished velouté through a chinois, pressing gently. The strained sauce should be ivory-coloured and flow in a smooth, silky ribbon from the ladle.