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Butter — unsalted, and a lot of it. Cultured butter for finishing.
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Dijon mustard, white and red wine vinegar, cornichons, capers.
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Shallots, garlic, thyme, bay, parsley, tarragon, chervil.
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Dry white wine, red wine, brandy, vermouth.
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Crème fraîche, heavy cream, gruyère, comté.
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Good stock — the single most French thing in any kitchen.