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Rinse and dry the chicken pieces. Rub the bone-in, skin-on chicken pieces with salt and pepper. Set aside.
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Heat the olive oil over medium high heat in a large skillet or Dutch oven with a lid. Brown the chorizo pieces in the oil and then remove with a slotted spoon.
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Add the chicken pieces to the oil and brown on both sides, about 7 minutes per side.
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Remove the chicken pieces to a large bowl. Pour off all but 1-2 tablespoons of oil.
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Add the onions to the pan with a pinch of salt. Also add a splash of white wine vinegar to help scrape up the tasty, browned bits stuck to the bottom of the pan.
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Sauté the onions, stirring occasionally, for 7 minutes, or until softened and starting to brown. Add the ground spices and toss, roasting, for 30 seconds. Add the saffron with the soaking water and cook for another 30 seconds.
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Measure the liquids by pouring the pomegranate balsamic vinegar to the 1/3 cup line in a liquid measuring cup. Add the 2 tablespoons of pomegranate molasses into the measuring cup. Then fill with white wine vinegar to the 1-cup measuring line. Add this liquid to the pan, once again scraping the bottom to removed any browned bits stuck to the pan. Add the lemon juice and chicken stock and bring to a boil. When the liquid boils, add the chorizo back into the pan. Then add the chicken pieces, skin side down. Cover tightly and reduce to simmer gently.
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Let simmer for 20 minutes, then flip the chicken pieces over so that they are skin side up. Cover and let simmer gently for 10 minutes.
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Remove the lid, and turn the heat up a bit so that the chicken continues to simmer. Simmer for another 5-15 minutes, until the chicken registers 165 F with a meat thermometer. Serve with potatoes, rice or couscous (I used Israeli couscous).