In a large pot, heat 1 tbsp butter over medium heat. Add ground beef and cook until browned. Drain any excess fat and set aside.
In the same pot, melt the remaining butter. Add chopped onion and minced garlic, sautéing until fragrant (about 3 minutes).
Stir in the flour and cook for 1-2 minutes to thicken the soup base.
Gradually add the beef broth while stirring to prevent lumps. Add diced potatoes and bring the soup to a simmer. Cook for 15-20 minutes, until potatoes are tender.
Stir in milk, salt, pepper, paprika, and thyme. Simmer for another 5 minutes.
Add shredded cheddar cheese and sour cream, stirring until melted and smooth.
Return the cooked ground beef to the pot and mix. Taste and adjust seasoning if necessary.
Serve hot, garnished with fresh parsley if desired.