In a bowl, combine the olive oil, melted butter, minced garlic, salt, pepper, chopped rosemary, thyme, and parsley. Whisk until well blended.
Place the chicken thighs in a large resealable plastic bag or dish. Pour the marinade over the chicken and refrigerate for at least 30 minutes, or up to 4 hours.
Preheat your oven to 425°F (220°C).
Remove the chicken from the marinade and place in a roasting pan skin-side up. Sprinkle leftover garlic and herbs on top.
Roast the chicken for about 35-45 minutes, until the skin is golden brown and the internal temperature reaches 165°F (75°C).
Remove the chicken and make the sauce by adding chicken broth to the pan. Whisk in cornstarch and cook until thickened.
Squeeze fresh lemon juice over the sauce and stir in more chopped parsley.
Drizzle the sauce over the chicken and serve hot with your favorite sides.