Place the chicken thighs, carrots, celery, onion, butternut squash, and potatoes in the slow cooker. Pour in the chicken broth and add the dried thyme along with salt and black pepper. Stir once to combine.
Cover and cook on low for 6 to 7 hours until the chicken is tender and the vegetables are soft.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir the stew gently.
In a mixing bowl, whisk together the flour, baking powder, and 1/2 teaspoon salt. Stir in the chopped parsley, then add the milk and melted butter. Mix just until a soft dough forms.
Drop spoonfuls of the dough onto the surface of the hot stew. Cover and cook on high for 1 hour without lifting the lid until the dumplings are firm and cooked through.