Brown ground beef in a skillet over medium-high heat. Drain excess fat. Add onion and garlic, cooking until onions are translucent.
Transfer beef mixture to crockpot and add potatoes, carrots, and celery.
Pour in broth and add seasonings (thyme, parsley, paprika, salt, and pepper).
Cover and cook on low for 6-8 hours or high for 3-4 hours until vegetables are tender.
In the final 20 minutes, stir in cream, cheese, and milk. Add cornstarch mixture if desired.
Serve hot, garnished with fresh parsley and extra cheese.