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1
Submerge the brains in a large bowl of cold water. Leave for 2–3 hours, changing the water several times. The water runs progressively cleaner and the tissue visibly firms.
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2
Under gently running cold water, peel away the outer membrane — the thin, vein-threaded layer covering each brain — working carefully with the fingertips. Remove it in its entirety. The surface beneath is smooth, cream-coloured, and unmarked.
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3
Combine the court-bouillon ingredients in a wide saucepan and bring to a steady 75–80 °C — a bare tremble at the surface, no rolling boil. Lower the brains in gently and poach for 15–20 minutes. This is where the dish lives or dies: a vigorous boil will cause the soft tissue to disintegrate beyond recovery; the correct temperature yields brains that are uniformly firm to the touch yet still yielding under light pressure.
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4
Lift the brains from the court-bouillon and refresh them in the same liquid, off the heat, until cooled. Do not use ice water — thermal shock cracks the soft tissue. Drain, pat dry with a clean cloth, and cut into slices 2 cm thick.
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5
Season the slices on both sides with salt and white pepper. Dredge lightly in flour, shaking off any excess. The surface should appear finely, evenly dusted — no clumps.
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6
Heat the clarified butter in a wide sauté pan over moderate heat — not high. Place the slices in without crowding and sauté for 2 minutes per side, turning once only and with care. The crust is golden and the slices hold their shape without sticking. Transfer immediately to a warm plate.
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7
Wipe the pan clean. Add the 50 g of fresh butter and cook over moderate heat until it turns hazelnut-brown — beurre noisette — with a nutty aroma rising from the pan. Add the lemon juice and capers, stir once, then add the chopped parsley. Pour the sizzling butter over the brains without delay.