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1
Assemble the onion piqué: press the bay leaf and two cloves firmly into the cut face of the half-onion so they will not float free during simmering. Set aside. Heat the milk in a separate saucepan until it steams and is on the point of simmering; keep it hot.
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2
Melt the butter in a heavy saucepan over gentle heat. Add the flour all at once and stir continuously with a wooden spatula, pressing the paste against the base of the pan. Cook for 2–3 minutes — the roux is ready when it froths, smells faintly of biscuit, and has developed no colour whatsoever: it must remain pure white.
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3
This is the step on which the dish lives or dies. Remove the pan briefly from the heat. Add a small splash of hot milk and whisk vigorously until a perfectly smooth paste forms — no lumps, no streaks. Return to gentle heat, add roughly one-third of the remaining hot milk and whisk until homogeneous. Pour in the rest in a steady stream, whisking constantly, until the sauce is fully combined and beginning to thicken.
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4
Bring the sauce to a gentle simmer, then submerge the onion piqué. Cook, uncovered, for 30–45 minutes over the lowest possible heat, stirring every few minutes with the spatula to prevent the base from catching. The sauce is ready when it pours like thick cream, coats the back of a spoon evenly, and tastes entirely of butter and warm milk — no trace of raw flour should remain.
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5
Remove and discard the onion piqué. Pass the béchamel through a fine chinois into a clean saucepan. Season with fine salt, white pepper, and a fresh grating of nutmeg. If finishing with monter au beurre, whisk in the cold butter in one piece off the heat; the surface should appear glossy and the texture fluid.