In a large pot or Dutch oven over medium-high heat, cook the ground beef, breaking it into crumbles, until fully browned. Drain any excess fat.
Add the diced onion and cook for 3-4 minutes until softened. Stir in the minced garlic and cook for 30 seconds until fragrant.
Add the butter and let it melt. Sprinkle the flour over the beef and onion mixture and stir to coat. Cook for 1 minute.
Pour in the beef broth while stirring to prevent lumps. Add the diced potatoes, paprika, garlic powder, and onion powder. Stir to combine.
Bring to a boil, then reduce heat to medium-low. Simmer for 15-18 minutes until the potatoes are fork-tender.
Stir in the milk and heavy cream. Let the soup heat through for 2-3 minutes.
Remove from heat and stir in the shredded cheddar cheese until fully melted and smooth. Season with salt and pepper to taste.
Ladle into bowls and top with extra cheddar, a dollop of sour cream, and chopped chives. Serve with crusty bread.