In a skillet, brown ground beef over medium-high heat until no longer pink. Drain excess fat, then add chopped onion and minced garlic. Sauté for about 5 minutes.
Transfer beef mixture to crockpot, add diced potatoes, carrots, and celery.
Pour in broth, add thyme, parsley, paprika, salt, and pepper. Stir to combine.
Cover and cook on low for 6-8 hours (or high for 3-4 hours) until veggies are tender.
Stir in heavy cream, cheddar, and milk. For a thicker soup, mix in cornstarch mixture. Cook on low for another 15-20 minutes.
Ladle into bowls, garnish with parsley and extra cheese, if desired.
