Season the chicken liberally with salt and pepper. In a large skillet, heat the oil over medium-high heat. Carefully place chicken, skin side down, into the hot skillet. Cook until golden brown, about 5 minutes. Turn the chicken and cook until the underside is golden, another 3 to 4 minutes. Remove the chicken from the skillet and set it aside. Reduce the heat to medium. To the same skillet add onions and mushrooms and cook, stirring, about 4 minutes. Add garlic, rosemary, and thyme leaves and cook until fragrant, 30 seconds. Stir in flour and cook for another minute. Slowly pour in chicken broth and mix well. Season with salt and pepper to taste and return the chicken to the skillet, skin side up. Reduce heat to a simmer, cover, and cook the chicken until it reached an internal temperature of 165°F. Finish with fresh parsley. Serve immediately or store in the refrigerator for up to 3 days.