Prepare the slow cooker by lightly greasing the insert.
In a large skillet over medium heat, cook the ground beef until browned, breaking it apart as it cooks, then drain excess fat.
Transfer the browned beef to the slow cooker.
Add the onion, garlic, potatoes, carrots, celery, corn, beef broth, Italian seasoning, smoked paprika, salt, and black pepper to the slow cooker, stirring to combine.
Cover and cook on Low for 6–7 hours or High for 3–4 hours, until vegetables are tender.
About 30 minutes before serving, melt the butter in a medium saucepan over medium heat. Whisk in the flour to form a roux and cook for 1–2 minutes.
Slowly whisk in the milk or cream until smooth and slightly thickened.
Stir the roux mixture and shredded cheddar cheese into the slow cooker, mixing until well combined and creamy.
Cover and cook for the remaining 30 minutes to heat through and thicken.
Garnish each bowl with fresh chopped parsley before serving.