Place the chicken thighs, sliced mushrooms, chopped onion, sliced carrots, chicken broth, thyme sprigs, minced garlic, salt, and pepper into the slow cooker.
Cover and cook on low for 6 to 7 hours until the chicken is very tender.
Remove the chicken thighs to a plate and shred them with two forks.
Return the shredded chicken to the slow cooker and discard the thyme stems.
Stir in the heavy cream until the soup is evenly combined.
Ladle into bowls and top each serving with chopped parsley.