Melt 2 tablespoons butter in a large oven-proof skillet over medium-high heat. Add chicken, skin-side down, and sear both sides until golden brown. Drain excess fat and set aside.
Melt 1 tablespoon of butter in the skillet. Add garlic. Stir until fragrant, then add chicken broth, heavy cream, sun-dried tomatoes, dried oregano, dried thyme, and fresh basil and reduce heat to low. Return chicken to the skillet and baste well.
Bake at 400˚F (200˚C) for 25 minutes.
Serve immediately and drizzle remaining broth mix over chicken.