Preheat oven to 325 degrees.
Wash and pat dry chicken thighs. Sprinkle with flour, salt, and pepper.
Preheat a large saute pan or dutch oven that has a light fitting lid to a medium to medium-high heat.
Add olive oil and butter. When butter foams and starts to brown, add chicken thighs skin side down. The chicken should sizzle when touching the oil.
Cook until browned, about 5-7 minutes. Flip and cook and additional 1-2 minutes.
While chicken is browning, separate the garlic cloves from the garlic head and place in a large bowl.
Fit another bowl over the first and shake vigorously for 2-3 minutes. Remove peels/papers from cloves.
Remove browned chicken from pan. Drain excess drippings, if necessary, until about 2 tablespoons remain.
Saute garlic cloves in the drippings for 2-3 minutes until they begin to soften and brown. Remove cloves to the plate with the chicken.
Add the wine, parsley, and thyme to the pan, making sure to scrape up all the bits stuck to the bottom. Cook at a low simmer until the liquid has reduced by half.
Add the stock and bring temp up to a low boil. Turn off burner and add the chicken, skin side up, along with the garlic cloves making sure there is garlic both under and on top of the chicken thighs. The majority of the skin on the thigh should be above the liquid in the bottom of the pan.
Cover with a tight fitting lid and place in preheated oven. Bake covered for 20 minutes.
Remove the lid and continue to bake for 20-30 minutes until chicken is cooked through and skin and exposed garlic are golden.
Remove pan from oven and place chicken thighs and about half the garlic cloves on a plate loosely tented with foil.
Place the pan back on the burner and bring liquid to a low simmer.
In a medium bowl, mix the flour and butter into a smooth paste. Add 1/2 cup of the hot liquid and whisk to combine until smooth. Add the flour mixture and the cream to the boiling liquid, whisking to combine.
Simmer for 3-5 minutes to thicken sauce and cook flour. Taste test the sauce to check seasoning. A small amount of salt and pepper may be desired.
Stir in fresh parsley reserving a pinch for garnish.
Serve with sliced crusty bread, mashed potatoes, rice, or pasta if desired.