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1
Toast the shelled walnuts in a dry pan over medium heat, stirring constantly, until fragrant and lightly coloured, then transfer them immediately to a food processor so the residual heat does not carry them past the point where bitterness sharpens and the oils turn acrid. Grind until the walnuts release their oils and the mass becomes a smooth, cohesive paste — no visible pieces should remain. The paste is ready when it resembles a dense, oily dough.
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2
In a heavy pot, soften the onion in a little oil over medium heat until translucent and beginning to colour. Season the chicken or duck pieces with turmeric and salt, add them to the pot, and brown on all sides so that the exterior develops a crust that will hold the meat together through the long braise ahead. Remove the meat and set aside.
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3
Add the walnut paste to the same pot so that it lifts the browned residue left by the meat and absorbs those deeper flavours into the sauce from the very beginning. Pour in the 500 ml of water and stir to combine fully, then bring to a gentle simmer and cook uncovered, stirring periodically, for 30 minutes. At the end of this stage the raw bitterness of the walnuts will have mellowed and the liquid will have taken on a pale, creamy-brown colour.
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4
Return the browned meat to the pot, then begin adding the pomegranate molasses in stages — pour in roughly one-third, stir thoroughly, and taste — so you can feel the balance shifting and stop at exactly the point where the sweet-sour-bitter character holds in equilibrium and no single element dominates. This calibration is where the dish lives or dies: too much molasses and the tartness overwhelms; too little and the walnut bitterness is unmediated. Once balanced, partially cover the pot and cook over the lowest possible heat for 2 to 2½ hours, stirring every 20 minutes to prevent the walnut paste from scorching on the base.
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5
After 2 hours, assess the colour: the sauce should be deep mahogany to reddish-brown, because that depth of colour signals that the walnut paste has fully cooked out and the sauce has the round, almost chocolate-like weight that defines the dish. A pale sauce indicates insufficient cooking; continue at the same low heat until the colour deepens. The surface will show an oily sheen as the walnut fat separates slightly — this is correct.
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6
In the final 15 minutes, adjust sweetness with sugar if required, adding it only now so that introducing it earlier does not suppress the natural darkening of the sauce. Taste once more for the sweet-sour-bitter balance; if the stew is sharply sour, stir in the fresh pomegranate seeds rather than additional sugar, as their brightness lifts the acidity without tipping the sauce toward sweetness. The finished sauce coats the back of a spoon in a thick, glossy layer.
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7
Serve immediately over white rice with tahdig. The sauce should fall slowly from the spoon and hold its gloss on the plate.