Add 2 cups of water to a saucepan and bring to a boil. Separate garlic cloves (you don't need to peel them) and add to the water. Cook for 1 minute, then drain and peel garlic.
Pat the chicken pieces dry with paper towels and season well with salt and pepper on both sides. Heat a very large deep (preferably cast iron) pan or skillet over medium heat. Add 2 Tablespoons butter and oil until hot.
Add chicken, skin side down and cook for 5 minutes, until the skin is golden brown. Flip and cook on the other side for 3 minutes.
Add garlic cloves around the chicken and add thyme and bay leaf.
Cover the skillet and cook over med-low heat for 15-20 minutes or until the chicken is cooked through and the juices run clear when pierced with a fork. Transfer the chicken and garlic to a platter and cover with foil to keep warm. Discard the bay leaf.
Turn the skillet heat to medium-high and add the wine. Cook until the liquid has reduced by half, about 5 minutes.
Whisk the cornstarch into the chicken stock and add to the pan. Cook until the sauce has slightly thickened, 2-3 minutes. Taste and season with additional salt and pepper, or herbs, as needed.
Remove from heat and stir in remaining 2 Tablespoons of butter. Place the chicken on a serving platter and pour sauce over the chicken.
Serve with French green beans and a toasted baguette for spreading the cooked garlic cloves on.