Score and season the duck breasts: Using a sharp knife, score the skin of the duck breasts in a crisscross pattern, being careful not to cut into the meat. Season the duck generously with salt, pepper, and half of the minced thyme.
Sear the duck: Heat a large, oven-safe skillet over medium heat. Place the duck breasts skin-side down in the skillet and sear for 5-7 minutes until the skin is golden brown and crispy. Flip the duck breasts and cook for an additional 3-4 minutes.
Finish in the oven: Preheat the oven to 375°F (190°C). Transfer the skillet to the oven and roast the duck for 7-10 minutes, depending on your preferred doneness. Remove from the oven and let the duck rest while you prepare the sauce.
Prepare the orange thyme sauce: In the same skillet, drain some of the excess fat, leaving about 1 tablespoon. Over medium heat, add the minced garlic and remaining thyme. Sauté for 1-2 minutes until fragrant. Add the orange zest, chicken broth, and white wine (if using). Let the sauce simmer for 3-4 minutes, allowing it to reduce. Stir in the butter and adjust seasoning with salt and pepper.
Serve: Slice the duck breasts and serve them drizzled with the orange thyme sauce. Garnish with fresh thyme sprigs and a small amount of orange zest for extra flavor.