Adjust oven to middle rack and heat to 450 degrees. Whisk 2 tablespoons broth and the cornstarch together in a small bowl and set aside. Combine remaining broth, wine, garlic, and thyme in large measuring cup.
Pat chicken dry. Salt and pepper pieces. Heat oil in oven-safe skillet over medium high heat until just smoking. Cook chicken until well browned on both sides.
Slowly pour broth mixture into skillet and bring to boil. Transfer skillet to oven and roast until dark meat registers 175 degrees, 12 to 18 minutes. Transfer chicken to plate and tent with foil. Discard garlic.
Pour pan juice into liquid measuring cup and skim fat. Return pan juices to now empty pan and bring to boil. Reduce for 5 minutes. Add reserved cornstarch mixture and cook 2 more minutes. Off heat, mix in butter. Serve