Pat the duck breasts completely dry. Score the skin in a shallow crosshatch pattern without cutting into the meat. Season both sides with salt and black pepper.

In a small bowl, whisk together honey, soy sauce, apple cider vinegar, chicken broth, garlic, ginger, and Dijon mustard. Set aside.

Place the duck breasts skin-side down in a cold, dry heavy skillet. Set the heat to medium-low and cook for 10–14 minutes, pouring excess rendered fat into a heatproof container as needed, until the skin is golden and crisp.

Flip the duck and cook the meat side for approximately 6–10 minutes, or longer if needed, until an instant-read thermometer inserted in the thickest part reaches 165°F (74°C), the USDA safe minimum temperature for poultry. Lower the heat if the exterior browns too quickly.

Transfer the duck to a clean plate, skin-side up, and rest for 5 minutes. Prepare the sauce while it rests.

Pour off excess fat from the skillet, leaving about 1 teaspoon. Add the honey mixture over medium-low heat, scrape up the browned bits, and simmer gently for 3–5 minutes until glossy and lightly thickened.

Remove the skillet from the heat and stir in the butter. If the sauce becomes too thick, loosen it with a small splash of broth or water.

Slice the duck against the grain. Arrange slices skin-side up and spoon the warm honey sauce around or beneath the meat to preserve the crispy skin.

Garnish with thyme if desired and serve immediately.