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1
Melt the butter in a heavy saucepan over medium heat. Add the flour all at once and stir constantly for 2 minutes, until the roux smells biscuity and the colour deepens very slightly from pale to the faintest gold. The raw-flour smell must be gone before any stock is added.
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2
Add the hot stock in three stages, whisking until completely smooth after each addition. A cold or all-at-once addition will produce lumps that cannot be fully corrected. The sauce will look thin at this point; this is correct.
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3
Bring the sauce to a simmer, then reduce the heat to the lowest flame that maintains a lazy, intermittent bubble. Simmer for a minimum of 20 minutes. Throughout this period, skim the surface frequently — the roux releases impurities that must be removed for a clean, glossy result. At the end of simmering the sauce should coat a spoon in a thin, even film with no floury residue on the palate.
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4
This is where the dish lives or dies: if making the allemande or any egg-enriched variant, whisk the yolks and cream together in a bowl, then temper by beating a ladleful of the hot velouté into the liaison before adding the mixture back to the pan. From this point the sauce must never return to the boil — a single boil will curdle the yolks irreversibly, breaking the sauce beyond recovery. Stir over gentle heat until the sauce thickens perceptibly and coats the spoon in a heavier, more opaque layer.
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5
Remove from the heat and mount with the cold butter pieces, swirling the pan or whisking gently until each piece is absorbed and the surface carries a light gloss. The sauce is ready when it falls from the spoon in a slow, unbroken ribbon.