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Take the goat neck out of the marinade, reserving the marinade. Heat a smoker to 230 degrees F with seasoned oak or hickory wood. Put the goat neck in the smoker and cook, maintaining the temperature and brushing with the reserved marinade every 90 minutes, until a dark golden bark has evenly formed on the outside of the neck, about 4 1/2 hours.
Preheat the oven to 325 degrees F. Put the smoked goat neck in a deep pan or pot and pour the marinade into the pan until it is covering two-thirds of the neck. Wrap the pot tightly with aluminum foil and cook until fork-tender, about 4 hours. (At this point, it can be finished to eat or refrigerated for up to 4 days.)
Put the butter in a saute pan and turn to medium heat. Once the butter liquefies, transfer the goat neck to the pan and baste it with the butter using a sauce spoon. When the butter turns golden brown, deglaze with the white wine and add the dried cherries. When the white wine has reduced by half, mix in 2/3 cup of the goat marinade and continue to baste the goat until the mixture forms a thick enough sauce to evenly coat the back of the spoon.
Place the goat neck on a plate by itself or over a bed of rice. (In the restaurant we serve it on top of a bed of coconut rice that we gently toss in Indian cow ghee.) Spoon the pan sauce evenly over the goat and finish with chopped cilantro or mint if using.