1. Place 1 cup flour in a large bowl. Season chicken with salt and pepper, and toss in flour to coat evenly. Transfer chicken to a platter, and set aside.

2. Heat a large Dutch oven over medium heat. Add the reserved chicken skin, and cook, stirring occasionally, until fat has been rendered and skin is golden brown and crisp. Discard skin. Remove all but 2 tablespoons of fat from pot. (Alternatively, if desired, use olive oil, heating until it is hot but not smoking.)

3. Add half the chicken to the pot, and cook, turning occasionally with tongs, until well browned on all sides, about 5 minutes. Transfer to a platter; set aside. Repeat with remaining chicken. Add onion to pot; cook, stirring occasionally, until onion is translucent, about 4 minutes. Add garlic and mushrooms; cook, stirring, until vegetables are tender, about 5 minutes more. Raise heat to medium-high. Add the wine; scrape any browned bits from the bottom of the pot with a wooden spoon. Cook until most of the liquid has evaporated.

4. Add stock, tomatoes with reserved juice, bay leaf, oregano, and rosemary to pot; stir to combine. Using tongs, return chicken to pot along with any juices that have accumulated on the platter. Submerge chicken in sauce. Bring to a gentle simmer, cover, and cook until the chicken is cooked through and very tender, about 30 minutes.

5. In a small bowl, mix together the butter and remaining 1 1/2 tablespoons flour to form a smooth paste. Stir half the paste into the simmering stew, and cook about 3 minutes. If the stew is still not as thick as desired, stir in the remaining paste, and cook 3 minutes more. Remove and discard bay leaf; serve stew hot over warm polenta. Stew can be refrigerated up to 3 days or frozen up to 1 month in an airtight container. Cool completely before storing.