Brown the ground beef in a skillet over medium heat until fully cooked. Drain any excess grease.
Transfer the cooked beef to the slow cooker.
Add the diced potatoes, onion, celery, garlic, chicken broth, thyme, parsley, smoked paprika, salt, and pepper.
Cover and cook on Low for 6 to 8 hours or High for 3 to 4 hours, until the potatoes are tender.
Mix the cornstarch with the cold water until smooth.
Stir the cornstarch slurry into the soup along with the heavy cream.
Add the shredded cheddar cheese and stir until melted.
Cover and cook for another 20 to 30 minutes, until the soup has thickened.
Taste and adjust the seasoning if needed.
Garnish with chopped parsley before serving.