In a medium pot, cook wild rice according to package directions. I recommend adding ½ broth and ½ water for the liquid amounts to increase flavor if you have more broth on hand.
Meanwhile in a large, heavy pan, melt 1 tablespoon of butter or heat olive oil to medium heat. Add bite sized pieces of boneless, skinless chicken thighs, season with salt and pepper, and brown on both sides till just cooked through - about 6-7 minutes. Increase heat as needed to get it nicely browned. Remove 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. Deglaze the pan with broth, scraping any browned bits from the bottom, and bring to a boil. Turn down the heat and add cooked chicken, dijon, thyme, and rosemary, and continue to simmer until the liquid is reduced, about 5 minutes. If using, add the heavy cream and simmer another 5 minutes (10 minutes total). The sauce will not be super thick, but still slightly thickened from where you started. Taste and adjust any seasonings.
In a large serving bowl, layer cooked wild rice and top with the chicken and dijon sauce. Top with any remaining rosemary for garnish.