Preheat the oven to 350 degrees F. Heat a large skillet over medium-high heat. Season the chicken with salt and pepper and coat in flour, shaking off the excess. Add 2 tablespoons vegetable oil to the pan. Place the chicken smooth-side down in the skillet and cook until golden, about 5 minutes per side. Transfer to a baking dish and bake until cooked through, about 8 minutes.
Meanwhile, add the red onion and apple to the skillet, along with 1 tablespoon vegetable oil if the pan is dry. Increase the heat to high and cook, tossing, until the onion has wilted slightly and the apple is golden brown, about 2 minutes. Stir in the vinegar with a wooden spoon, scraping up the browned bits from the pan. Let the mixture boil until the vinegar becomes syrupy, about 1 minute. Add the chicken broth and bring to a boil. Cook until the broth reduces by half. Remove from the heat, season with salt and pepper and whisk in the butter.
Remove the chicken from the oven; add any collected juices to the pan sauce. Divide the chicken among plates and spoon the apple, onion and sauce over each piece. Sprinkle with the parsley.
Photograph by Antonis Achilleos
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