Preheat the oven to 350℉.
Pat dry the chicken. Salt and pepper liberally and set aside.
In a large ovenproof pan over medium heat, cook the whole garlic cloves in olive oil and butter, stirring occasionally until lightly golden, about 5-10 minutes. Don’t let them burn or get too brown. Remove the garlic from the pan and set aside.
Increase the heat to medium high. Add the chicken skin-side down and brown until the skin is golden and crispy, about 5 minutes. Turn the chicken over and sprinkle herbes de Provence over the crispy skin. Add the garlic back to the pan and place hot pan in the oven.
Bake the chicken until cooked through, about 35-45 minutes. Once the chicken is done, remove chicken and garlic to a platter.
Place the pan over medium-high heat and sprinkle flour over the drippings and whisk together. Deglaze the pan with the stock and lemon juice and heat until the gravy boils. Pour the sauce over the chicken on the platter and serve.