Place the beef, carrots, parsnips, potatoes, onion, and garlic in the slow cooker.
In a small bowl, whisk the beef broth, balsamic vinegar, tomato paste, thyme, salt, and pepper until smooth.
Pour the broth mixture over the ingredients in the slow cooker and stir gently to combine.
Cover and cook on low for 8 hours or on high for 4 to 5 hours, until the beef is tender and the vegetables are soft.
Stir the stew once more, then ladle into bowls and top with fresh parsley before serving.