Bring a small saucepan of water to a boil. Separate head of garlic into individual cloves. Add to boiling water and cook 1 1/2 minutes, or until skin peels off easily. Drain and rinse briefly under cold running water. Peel garlic cloves. Trim any pieces of fat or extra skin from chicken; rinse pieces and pat dry. Season liberally with salt and pepper. In a large skillet, heat oil over medium-high heat. Add chicken, skin side down, and saute until skin is nicely browned, 8 to 10 minutes. Carefully holding lid against pan, pour off all but a thin film of fat. Turn chicken over and sprinkle onion between pieces. Cover and cook 5 minutes. Pour in wine and bring to a boil, stirring with a wooden spoon to scrape up any brown bits on bottom or around sides of pan. Boil until wine is reduced to 2 or 3 tablespoons, about 2 minutes. Scatter garlic around chicken, season with thyme and pour broth into pan. Cover, bring to a boil, reduce heat to low and simmer 25 minutes, or until chicken is very tender. Remove chicken and half of garlic cloves to a deep platter or serving dish. Skim fat off sauce in pan. Pour sauce into a blender or food processor and puree until smooth. If sauce is too liquid, pour into a small saucepan and bring to a boil. Dissolve cornstarch in 1 tablespoon cold water and stir into sauce. Cook, stirring, 1 minute, until slightly thickened. Season sauce with additional salt and pepper to taste. Pour over chicken and serve.
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