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heat 1 tablespoon butter in a large skillet over medium-high heat.
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cook the sausage until golden, about 2 minutes.
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season the chicken with salt and pepper, then toss with the flour in a bowl; add to the skillet and cook until browned but not cooked through, about 3 minutes.
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add the onion, peppers, garlic, 1/2 teaspoon salt, and pepper to taste and cook 3 minutes.
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add the wine, scraping up any browned bits; bring to a boil and cook until slightly reduced, about 1 minute.
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add the broth and bring to a gentle simmer.
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cover and cook until the sausage and chicken are cooked through, about 5 minutes.
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increase the heat to high and stir the parsley and cherry peppers and their liquid into the skillet; boil until reduced by one-third, 2 to 3 minutes.