For a faster cook time - In a medium pot, cook wild rice according to package directions. I recommend adding 1/2 broth and 1/2 water for the liquid amounts to increase flavor if you have more broth on hand. Season with kosher salt and black pepper to taste. For a one-pan dinner - Use a large skillet with a lid and steam the rice in the pan before removing it to sear the chicken.
In a large cast iron skillet, add 1 tablespoon of butter or olive oil over medium high heat. Add the chicken thigh pieces to the skillet and, season with 1/2 teaspoon kosher salt and 1/8th teaspoon black pepper, and brown the chicken on both sides till just cooked through - about 7-8 minutes. Increase the heat as needed to get it nicely browned. Remove the chicken pieces from the pan and set aside.
In the same pan, add other tablespoon of butter or olive oil. Add carrots, shallots, and apples plus a pinch of salt and pepper, cooking over medium heat till softened, about 5-6 minutes.
Add the broth to the pan, scraping any browned bits from the bottom with a wood spoon, and bring the broth mixture to a boil. Add the thyme and rosemary, and continue to simmer until the liquid is reduced, about 5 minutes. Turn down the heat to medium and whisk in the dijon mustard and add in the cooked chicken. If using, add the heavy cream and simmer another 5 minutes (10 minutes total). The sauce will be thin but that's ok, it will be absorbed when the rice is added. Taste and adjust any seasonings.
Stir the wild rice into the skillet with the dijon chicken and top with any extra rosemary for garnish. Serve warm.
Notes
I use Lundberg Wild Rice Blend with 1 cup broth and 3/4 cup water for cooking. It yields roughly 3 1/2 cups cooked wild rice. You can add more or less to the skillet as you like (or have room for).
If you can't find honeycrisp apples, use another firm apple like pink lady so it retains it's texture well with cooking.
Chicken breast can be subbed for chicken thighs, but you may need to reduce the cooking time by 1-2 minutes.
Sulfite-free dijon mustard is recommended. Maille makes a version of this, as does Whole Foods brand and Annies.