Drop the garlic into recently boiled water for about 1 minute. Remove with slotted spoon and carefully peel. This took about 5 minutes, but the result was perfectly peeled garlic.
Generously salt and pepper the chicken. Brown the chicken in butter and oil. Do this over medium heat so the oil/butter combo doesnt get too brown. Be sure not to crowd the pan give them some elbow room!
Remove to a platter and continue until the stove is splattered and all the chicken has had a turn in the pan.
Sautee the garlic in the oil/butter for about 5 minutes do not allow them to burn. Add the wine and stock and gently scrape up the bits of goodness on the bottom of the pan.
Return the chicken and all the juices to the pan, sprinkle with thyme, cover, and simmer on low for about 1-1/2 hours. I actually let the pan sit on the stove for another few hours before dinner which I think made the chicken falling off the bone tender. I suppose you could place it, covered, in a low heat oven for an hour also.
Once again, remove the chicken to a platter. At this point, I actually searched for the 20 cloves of garlic only to find they had cooked away .. there were a few small pieces left in the sauce, which I removed with a slotted spoon. Take about 1 Cup of hot liquid from the pan and whisk in ¼ C flour. Add ¼ C half and half and pour this slurry mixture back into the pan. Boil and stir for about 5 minutes. Return the chicken and bring up to temperature.