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1
In a large skillet or high-sided saute pan with a lid, heat the oil and butter over medium-high heat until the foam from the butter begins to subside. Season the chicken generously with salt and pepper, then put it in the pan skin-side down. Cook-resisting the urge to repeatedly poke, prod, and look underneath-until it doesn't stick to the pan and is golden brown, about 6 minutes.
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2
Flip the chicken over and cook for 5 minutes more. Transfer to a platter, then pour off all but about 2 tablespoons of the fat from the pan. Add the sausages and livers (if using) and cook over medium-high heat, stirring often and breaking up the meat, until browned, about 3 minutes. Reduce the heat to medium and add the onions and, if using, the peppers, celery, garlic, and cayenne. Cook, stirring occasionally, until the onions are softened, about 8 minutes. Add the rice and bay leaf and cook, stirring often, until the rice is lightly toasted, about 2 minutes.*
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3
Add the broth, stir to combine, then add the reserved chicken, skin-side up, and any accumulated juices. Bring to a boil, then reduce the heat and simmer, covered, until the chicken is just cooked through and the rice is tender, about 20 minutes (see Tip). Let the pan sit, covered, for 5 to 10 minutes after taking it off the heat. Taste the rice and stir in a little more salt and/or pepper, if needed, then sprinkle with parsley or scallions, if you like.
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4
Prepare up to * and refrigerate, covered, for up to 1 day. Let sit at room temperature for about 20 minutes before continuing with the recipe. You may need to add a few minutes to the cooking time.
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5
Serve hot or warm. It will keep, covered, in a 200u00b0F (90u00b0C) oven, for about 1 hour.
