Season chicken with salt and pepper.
Heat 2 tablespoons of oil in a heavy, deep, cast iron pan. Sear the chicken on both sides until golden, about 3-4 minutes on each side. Remove from the pan and set aside.
Add the remaining oil to the pan. Sauté the onion until translucent. Add in garlic and cook until it is fragrant (about 30 seconds). Add the peppers, carrot, mushrooms, and herbs and cook for 5 minutes until the vegetables begin to soften.
Pour in the wine (or water), and deglaze the pan (scrape up the browned bits from the bottom of the pan). Cook until wine is reduced (about 2 minutes).
Add the crushed tomatoes, Roma tomatoes, and the chili flakes. Season with salt and pepper (if needed). Return the chicken to the pan.
After mixing all of the ingredients together, cover with a lid, reduce the heat to low and simmer (stirring occasionally) for 40 minutes or until the meat is falling off the bone. Add the olives and let it simmer for another10 minutes. Garnish with parsley and serve over pasta.