1. Preheat oven to 350.
2. Pat the chicken parts dry with paper towels and sprinkle both sides liberally with salt and pepper. Place 1/2 cup flour in a bowl and dredge the chicken in the flour. In a large (12") ovenproof pot (a Dutch Oven would be best), heat the oil. Add the chicken in three batches (don't crowd!) and brown lightly over medium-high heat for 3-5 minutes on each side. Remove the chicken to a plate and continue until all the chicken is browned.
3. Add the whole garlic cloves, mushrooms and thyme to the pot and cook over medium heat for 5 minutes, stirring occasionally. Add the sherry and cook for one minute, scraping up the brown bits. Add the minced garlic and cook for 2 more minutes. Add the wine, chicken stock, 1 tablespoon salt, and 1 teaspoon pepper and bring to a simmer. Add the chicken (large pieces first), cover, and place in the middle of the oven for 30-35 minutes, until the chicken is cooked through (about 165 degrees on an instant-read thermometer).
4. Remove the chicken to a bowl and discard the thyme. With a fork, smash together the butter and 1/4 cup flour and add it to the sauce. Simmer, stirring constantly, over medium heat for 5 minutes, until slightly thickened. Season to taste - you will want to add salt and pepper as it should be highly seasoned. Put the chicken back in the sauce and serve hot.
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