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Toast walnuts in a dry skillet until fragrant; grind into a coarse paste.
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Heat oil and sauté onion and garlic until translucent.
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Stir in walnut paste, pomegranate molasses, sugar, saffron (optional), and water; bring to a simmer.
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Add mushrooms and cook, covered, until mushrooms are tender and sauce thickens, about 60 minutes.
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Season with salt and pepper; garnish with parsley and serve over rice.