Using a sharp knife, score the skin of the duck breasts in a crosshatch pattern, being careful not to cut into the meat. Season both sides generously with salt and pepper.

Place the duck breasts skin-side down in a cold skillet (cast iron is preferred). Turn the heat to medium-low.

Cook for 10 to 12 minutes without flipping. As the fat renders out, carefully spoon it out of the pan into a heat-proof bowl to keep the skin frying rather than boiling.

Once the skin is thin, crispy, and golden brown, flip the breasts and cook on the flesh side for 3 to 4 minutes for medium-rare (internal temperature of 135°F or 57°C).

Transfer the duck to a cutting board and let it rest for at least 10 minutes.

While the duck rests, prepare the sauce. Keep 1 tablespoon of duck fat in the pan and discard the rest. Sauté the minced shallot over medium heat for 1 minute.

Add the balsamic vinegar, chicken broth, cherries, honey, and thyme sprig. Simmer for 3 to 5 minutes until the sauce reduces and becomes syrupy.

Slice the duck breast thinly against the grain and serve topped with the warm cherry balsamic sauce.