Preheat oven to 400 degrees F. Season chicken on both sides with salt, pepper, 1 tablespoon of the rosemary, and 1 tablespoon of the thyme. Heat the olive oil over medium heat in a 12-inch cast iron skillet or very large oven-going skillet. Add chicken, skin side down, to the hot oil and cook for 5 to 7 minutes until browned on one side. Turn chicken pieces over and place skillet into the oven for 15 to 20 minutes or until done (at least 170 degrees F).
Remove chicken from skillet and set aside. Add mushrooms to skillet and turn heat to medium-high; cook stirring occasionally for 4 minutes. Add flour to skillet, stirring to coat. Stir in chicken broth, wine, and mustard. Cook and stir until thickened and bubbly. Cook and stir 1 minute more. Remove skillet from heat and add remaining rosemary, thyme, and parsley. Serve mushrooms sauce over chicken.