Place the chicken thighs, carrots, parsnips, potatoes, onion, and garlic in the slow cooker.
In a bowl, whisk the chicken broth with the flour, thyme, salt, and pepper until smooth. Pour the mixture over the ingredients in the slow cooker and tuck in the bay leaves.
Cover and cook on low for 7 hours.
Stir in the heavy cream, then cover and cook for 30 minutes more.
Remove the bay leaves. Serve the stew in bowls topped with chopped parsley.