Brown ground beef in a large soup pot over medium heat, then drain excess fat.
Add butter to the pot and melt completely.
Stir in chopped onion and cook until softened.
Add minced garlic and cook until fragrant.
Sprinkle flour over the mixture and stir well.
Slowly pour in chicken broth while stirring to avoid lumps.
Add diced carrots and potatoes to the pot.
Season with salt, black pepper, and paprika.
Bring to a boil, then reduce heat and simmer for 20 minutes.
Stir in milk and shredded cheddar cheese.
Cook until cheese is fully melted and soup is creamy.
Remove from heat and garnish with fresh parsley before serving.