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1
Place the salt cod in a large basin and cover generously with cold water. Soak for 48 hours, changing the water 6 times at regular intervals. The fish is sufficiently desalted when a small piece tasted raw is pleasantly saline rather than sharp.
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2
Drain the cod and place in a wide pan with the bay leaf and thyme. Cover with fresh cold water and bring to a bare shiver — 70–75 °C, never a boil. Hold at this temperature for 10 minutes. The flesh is done when it yields along its natural flakes at the touch of a finger but holds its structure; it must not be stringy.
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3
Lift the cod from the liquid. Remove every trace of skin and bone. Flake the flesh into a heavy-bottomed pan set over the gentlest possible heat. The flakes should be moist and still warm.
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4
This is where the dish lives or dies. With a wooden spoon, begin working the warm flaked cod vigorously. Add the warm olive oil in a thin, continuous stream, alternating with small additions of warm milk, beating hard after each addition as one would when building a mayonnaise. Continue for 15–20 minutes without interruption: the cod protein absorbs the fat and liquid and the mixture swells into a pale, smooth, voluminous cream. If the surface appears oily, introduce more milk; if it appears loose, introduce more oil. Cold oil or cold milk, added too quickly or without vigorous beating, will break the emulsion and cannot be recovered.
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5
Work in the garlic paste and white pepper. The finished brandade should be the consistency of very smooth mashed potatoes — ivory in colour, satiny from the emulsified oil, holding its shape cleanly on a spoon.
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6
Transfer the brandade to a gratin dish and spread level. Drizzle lightly with olive oil. Place under a hot grill for 3–4 minutes. The surface is ready when it carries an even, golden crust while the interior remains warm and creamy.
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7
Serve immediately from the gratin dish, accompanied by triangles of bread fried in olive oil and a few black olives alongside.