Melt butter in a large pot over medium heat. Add mushrooms, onion, and celery. Cook, stirring occasionally, until tender, about 8-10 minutes.
STEP 2
Stir in garlic and thyme until fragrant, about 1 minute.
STEP 3
Stir in chicken, chicken stock, wild rice, bay leaf, 1 teaspoon salt, and 1/2 teaspoon pepper. Bring to a boil; reduce heat and simmer, covered, until flavors have blended, about 20 minutes.
STEP 4
Stir in diced butternut squash or sweet potato; simmer, covered, until the chicken is cooked through and the rice is tender, about 15-20 minutes.
STEP 5
Remove chicken from the pot; shred it using two forks.
STEP 6
Stir in shredded chicken and kale until wilted, about 2 minutes. Stir in parsley; season with salt and pepper, to taste.