Wash the apples and cut each into fourths. Do not remove the skin. Cut away the seeds and core, then cut each quarter into four 1/2-inch-thick wedges. You should have a total of 16 wedges for each apple.
Place the flour in a shallow bowl. Dry the chicken breasts with paper towels and season with salt and pepper. Dredge each chicken breast in the flour to coat and transfer to a clean plate. Set aside.
Heat a large nonstick skillet over medium heat. Add 2 tablespoons of the butter and heat until melted. Add the apple slices, cut side down, to the hot skillet. Cook the apples until well browned, about 5 minutes per side. Transfer to a bowl and set aside.
Add the remaining 2 tablespoons butter to the now empty skillet. Once melted, add the chicken breasts and cook until well browned on both sides. Transfer back to the plate.
Immediately add the onion, thyme leaves and 1/2 teaspoon each salt and pepper to the hot skillet. Cook over medium heat until the onion is softened and browned, about 7-8 minutes.
Add the cider and broth (not vinegar yet) to the onions in the skillet and bring to a boil. Add the browned chicken to the skillet. Reduce the heat to medium-low, cover, and simmer until the chicken is cooked through, about 15 minutes. Do not turn the chicken.
Remove the chicken to a serving platter and tent with foil to keep warm. Add the cream to the skillet. Increase the heat to medium-high and bring to a boil. Cook until the sauce has thickened slightly, about 5 minutes. Add the vinegar and stir until combined. Add the apples, and any accumulated chicken juices to the skillet. Check the seasoning and add salt and pepper if needed. Spoon the sauce over the chicken breasts and garnish with parsley. Serve immediately.