Chicken Braised with 20 Cloves of Garlic

2 lg heads garlic
1 3 lb chicken -- cut-up
salt and freshly ground pepper
2 tbsp olive oil
1 small onion -- chopped
1/3 cup dry white wine or water
1 tsp dried thyme -- crumbled
2/3 cup chicken broth
1 tsp cornstarch -- optional

Bring a small saucepan of water to a boil. Separate heads of garlic into individual cloves. Add to boiling water and cook 1-1/2 minutes, or until skins peel 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, 8-10 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 tbsp, 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 tbsp of 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.