Preheat oven to 300ºF. Melt ghee in a large pot over medium heat. Add the onions to the pot along with 1/2 teaspoon sea salt. Cook until soft, about 5 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Stir in the thyme and coconut flour. Slowly whisk in the chicken stock and then scrape the bottom of the pot with a wooden spoon to release any browned bits.
Add the chicken breasts and squash and bring to a simmer. Cover the pot and place it in the oven for 1 1/4 hours.
Remove the pot from the oven and spoon out the chicken using a slotted spoon. Shred the chicken using two forks and then put the chicken back in the pot. Stir in the kale, cover and let stand for 5 minutes. Stir in parsley and season to taste with remaining 1/2 teaspoon sea salt and freshly ground pepper.