Rinse the wild rice and place it in a medium saucepan with the chicken stock, diced onion, and diced celery. Bring to a boil, then reduce to a simmer, cover, and cook for 45 minutes until the rice is tender and the liquid is absorbed.

While the rice cooks, score the duck skin in a crosshatch pattern and season both sides generously with kosher salt and black pepper. Let the duck sit at room temperature for 15 minutes.

Heat a large skillet over medium heat. Place the duck breasts skin side down and cook for 6 to 8 minutes until the skin is golden and much of the fat has rendered. Flip and cook 4 minutes more for medium-rare, then remove to a plate to rest.

Pour off all but 1 tablespoon of duck fat from the skillet. Add the minced shallot and cook 1 minute. Pour in the port wine, scraping the pan, then add the halved cherries. Simmer 3 to 4 minutes until the sauce thickens slightly.

Stir the butter into the cherry sauce until melted and glossy. Season with a pinch of salt and pepper if needed.

Fluff the wild rice pilaf and stir in the chopped pecans and fresh thyme leaves. Slice the duck breasts and serve over the pilaf with the cherry-port sauce spooned on top.