In a large cast-iron skillet, heat the olive oil and smashed garlic over medium-high heat. Add the chicken skin-side down and cook, turning once, for 10 minutes or until browned. Remove from pan and set aside. Discard the excess oil.
In the same skillet, add fresh olive oil and quartered garlic and sauté until translucent, about 2 minutes. Stir in the olives, capers, basil, and oregano and cook for 1 minute.
Stir in tomatoes and cook for 3 minutes. Season with salt, pepper, and chili flakes.
Return the chicken to the skillet, spooning the sauce over the pieces. Add the chicken stock, cover with an oven-safe lid or aluminum foil, and bake at 350° for 1 hour or until chicken is tender and cooked through.
Remove from the oven and sprinkle with additional fresh basil leaves. Serve hot.