In an ovenproof skillet over medium heat, brown the breasts skin side down with the garlic and thyme until the skin is crisp, 12 to 15 minutes. Season with salt and pepper. Pour the rendered fat into the skillet in which the potatoes are frying. Turn the breasts and continue cooking over medium heat for about 2 minutes. Transfer to the oven and bake until done to your liking (5 to 7 minutes for medium rare). Place the breasts on a plate, tent loosely with aluminum foil and let rest for 5 minutes. If desired, degrease the cooking juices in and deglaze the skillet with the sauce.