In a skillet, brown the ground beef with onion and garlic over medium heat until the beef is fully cooked. Drain any excess fat and transfer the beef mixture to the crockpot.
Place diced potatoes, carrots, and beef broth into the crockpot. Season with salt, pepper, and paprika, stirring to combine.
Cover and cook on low for 7-8 hours or on high for 4 hours, until the vegetables are tender and the flavors are well developed.
In a separate bowl, whisk together the milk and flour until smooth. Gradually add this mixture to the crockpot, stirring well to combine.
Stir in the shredded cheddar cheese until it melts and the soup becomes creamy. Adjust the seasoning to taste. Serve hot with your favorite crusty bread.