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1
Place the sliced white onions and butter in a heavy-based saucepan. Set over the lowest possible heat, cover with a lid, and sweat for 30–40 minutes without lifting the lid more than necessary. The onions are ready when they have entirely collapsed into a soft, translucent mass with no trace of colour at any edge — not a single brown spot.
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2
While the onions sweat, prepare a medium béchamel: melt the butter in a separate saucepan, add the flour and stir over moderate heat for 2 minutes until the roux smells biscuity but shows no colour. Add the milk gradually, whisking continuously, then simmer gently for 10 minutes until the roux is fully cooked out and the sauce coats the back of a spoon cleanly.
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3
Add the sweated onions to the finished béchamel. Simmer the two together over low heat for 15 minutes, stirring occasionally. The mixture is ready when the onions have fully dissolved into the sauce and the colour is uniformly ivory.
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4
Pass the sauce through a fine-mesh sieve, pressing all solids through with the back of a ladle, or blend and then sieve through a chinois to remove any onion fibres. The finished texture should resemble double cream — pourable but with distinct body. Any residual graininess means the sieving is incomplete.
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5
Season with white pepper and freshly grated nutmeg. Taste for salt. The sauce is complete when the flavour reads as gently sweet, faintly floral, and wholly without sharpness — a single note of caramel or roasted onion indicates the sweat step was not sufficiently gentle.