Pat the chicken dry and season all sides with the kosher salt and black pepper. Peel the garlic cloves, using the quick blanching method if desired: place separated cloves in boiling water for about 1 minute, cool them, and slip off the skins.

Heat the olive oil and butter in a large Dutch oven or heavy skillet over medium-high heat. Brown the chicken skin-side down in batches for about 5–7 minutes per side, then transfer it to a plate without crowding the pan.

Lower the heat to medium and add the peeled garlic cloves to the pan. Cook for 2–3 minutes, stirring gently, until the cloves are lightly golden but not dark brown or scorched.

If using flour, sprinkle it over the garlic and pan fat and stir for about 1 minute. Pour in the white wine, scraping the browned bits from the bottom, and simmer for 2–3 minutes.

Add the chicken stock, thyme, and bay leaf. Return the chicken to the pan skin-side up, arranging the pieces so they sit partly in the liquid while the skin remains exposed.

Cover the Dutch oven or skillet and simmer gently for 30–40 minutes. Cook until the chicken reaches at least 165°F in the thickest part and the garlic is very soft.

Remove the chicken and bay leaf from the pan. If you want a thicker sauce, simmer the liquid uncovered for several minutes, watching it closely so it reduces without drying out.

Stir in the heavy cream at the end if you want a richer sauce. Taste and adjust the seasoning only after reducing, since the stock and pan juices may already be salty.

Return the chicken to the sauce or spoon the sauce over the pieces. Finish with chopped parsley and serve immediately with crusty bread, mashed potatoes, rice, or noodles.