Place the chicken thighs in the bottom of the slow cooker. Add the sliced mushrooms, carrots, onion, celery, and potatoes on top.
Sprinkle the minced garlic, salt, and black pepper over the vegetables. Lay the thyme sprigs on top.
Pour the chicken broth over everything. Cover and cook on low for 6 to 7 hours until the chicken is tender and the vegetables are soft.
Remove the thyme sprigs. Shred the chicken directly in the slow cooker using two forks.
Stir in the heavy cream until the broth turns creamy and uniform. Let it cook for 10 more minutes on low before serving.