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1
Pour off all fat from the duck roasting pan, leaving only the dark fond. Set the pan over moderate heat and deglaze with a splash of the gastrique liquid (added in the next step), scraping every caramelised deposit from the base. Reserve.
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2
Make the gastrique: place the caster sugar in a small heavy saucepan over medium heat. Cook without stirring until it reaches a deep amber caramel. Remove from heat and carefully add the white wine vinegar — it will hiss violently. Return to heat and stir until the caramel dissolves completely into the vinegar. The gastrique is done when it is a uniform, glossy, bittersweet syrup.
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3
Blanch the orange zest strips twice: place in cold water, bring to the boil, drain, and repeat. This is the step that decides the sauce — under-blanched zest delivers a harsh, overwhelming bitterness that no amount of adjustment will correct; twice-blanched zest yields the clean, structural bitterness bigarade demands.
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4
Combine the deglazed fond, gastrique, Seville orange juice, and blanched zest strips in a saucepan. Add the demi-glace or reduced duck stock. Simmer gently to marry the elements. The sauce is ready when its flavour reads bitter first, sour second, and sweet last — the bitterness must lead.
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5
Strain the sauce through a fine sieve, discarding the spent zest strips. Cut the reserved length of twice-blanched zest into a hair-thin julienne of approximately 1 mm. Add the julienne to the finished sauce as garnish. The sauce is complete when the julienne is evenly distributed and the liquid is glossy and coating.