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1
Melt 1 tablespoon of the butter with 1 tablespoon of the oil in a skillet over medium heat. Add the minced onion, garlic, cumin, salt, and pepper, turn the heat down to low, and saute for about 10 minutes, until the onion softens. Transfer the mixture to a blender, then add the mint and cilantro, zests, juices, and rum and puree. Reserve 1/2 cup of the puree and use the rest to marinate the chicken for a few hours in the refrigerator.
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2
Preheat the oven to 400 F. Melt the remaining butter with the remaining oil in a large ovenproof skillet over medium heat. Add the chicken pieces, working in batches if necessary, and brown both sides, about 10 minutes.
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3
When nicely browned, transfer the chicken pieces with tongs to a plate. In the same skillet, cook the sliced onion gently for a few minutes, until slightly softened. Return the chicken to the skillet, skin side down, salt and pepper liberally, and pour the marinade over them. Transfer the skillet to the oven and bake for 30 minutes.
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4
Using tongs, flip each piece over, return to the oven, and bake for another 30 minutes, or until the chicken-especially thighs, if you're using them-is fully cooked. Remove the chicken and transfer to a serving platter. Pour the reserved 1/2 cup puree into the pan and mix it around with a spatula. Pour this sauce over the chicken. Serve with lime wedges and a small bowl of salt to pass around.
