Heat oil in a large skillet. Season the chicken with salt and black pepper. Add the chicken to the skillet, skin side down, and cook over moderately high heat until the skin is crisp and browned, about 8 minutes. Turn and cook for 3 minutes longer. Transfer the chicken to a baking sheet or large platter, skin side up.
2Add the onions and mushrooms to the skillet and cook over moderately high heat, stirring occasionally, until softened slightly, about 5 minutes.
Add the sage, bay leaves, and crushed red pepper to the skillet and cook, stirring occasionally, until the onions are golden and starting to stick to the bottom of the skillet, about 5 minutes.
3Add the apple cider to the skillet and simmer over moderately high heat until the cider is syrupy, about 25 minutes. Add the vinegar to the pan and simmer for 2 minutes. Season lightly with salt and black pepper. Stir stock and parsley into the skillet. Season lightly with salt and black pepper.
4Transfer the onion sauce to a large roasting pan. Arrange the chicken in the sauce, skin side up. Set the roasting pan in the oven and reduce the heat to 350°. Roast the chicken until cooked through, about 1 hour and 15 minutes.
5Transfer the chicken to a platter. Set the roasting pan over high heat and boil the sauce until the liquid is reduced, about 10 minutes. Season the sauce with salt and pepper and serve with the chicken.