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1
Set the oven to 220°C. Prick the duck skin all over with a fine needle, taking care not to pierce the flesh beneath. Season the bird liberally inside and out. Stuff the cavity with the orange half, thyme, and bay leaf. The skin should feel taut and dry to the touch before it enters the oven.
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2
Place the duck breast-up in a roasting pan and roast at 220°C for 20 minutes to establish the Maillard crust. Reduce the oven to 180°C and continue roasting for a further 35–45 minutes. The dish lives or dies here: the breast must reach 58–60°C at its thickest point (rosé) and the thigh 72°C — duck breast dries irreversibly above 65°C. Verify with an instant-read thermometer.
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3
Transfer the duck to a warm dish, tent loosely, and rest for 15 minutes. The juices, when the thigh is pierced at its joint, should run faintly pink.
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4
Meanwhile, blanch the julienned orange and lemon zest in boiling water. Drain, refresh, and repeat three times in total. The zest should taste clean and faintly bitter, not acrid.
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5
Pour off all but 1 tablespoon of duck fat from the roasting pan. In a separate heavy saucepan, cook the sugar dry over medium heat to a deep amber caramel at 170°C — the colour must be tawny gold, not dark brown. A burnt caramel cannot be rescued.
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6
Standing back, deglaze the caramel with the red wine vinegar — the violent reduction is expected. Add the juice of both Seville oranges and the lemon. Deglaze the roasting pan with the demi-glace, scraping up all sediment, and strain this liquid into the caramel-citrus base. Reduce over moderate heat until the sauce coats the back of a spoon (nappant). Stir in the blanched zest julienne. The finished sauce should be glossy, tawny-gold, and sweet-sour-bitter in precise equilibrium — taste and adjust.
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7
Carve the duck at the table. Spoon the sauce bigarade over each portion, distributing the zest julienne evenly.