Remove excess fat from chicken, rinse well inside and out and pat dry. Rub chickens with lemon inside and out and under skin of breasts. Rub with sea salt and set aside to marinate in a nonreactive baking dish, covered and refrigerated, overnight. Next day, rinse chickens again and pat dry.
In a flameproof casserole large enough to hold both chickens combine cilantro, parsley, garlic, ginger, saffron, preserved lemon and pepper to taste. Add 1/4 cup water and chickens, turning to coat thoroughly, and rubbing some of the mixture inside. Add reserved giblets, except livers. Pour oil over and bring to a simmer over low heat. When chicken begins to sizzle, add onions, cover and cook for 30 minutes. Add livers and paprika and continue to cook, covered, 1 hour more.
Remove chickens to a carving board and let rest, covered loosely with foil, while you finish the sauce. Cut giblets into small pieces and return to sauce. Using a fork, crush livers into sauce to thicken. Sauce should be thick -- if it is thin, boil until reduced and thickened. Add butter and olives. Heat, swirling pan, until sauce is emulsified. To serve, cut chickens into quarters and arrange on a warmed platter. Spoon sauce over and garnish with lemon peel.
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