1. Heat a large pot or Dutch oven over medium heat. Add the ground beef and diced onion. Cook, stirring and breaking up the beef, until the beef is browned and the onions are soft, about 6-8 minutes. Drain any extra fat. Stir in the minced garlic and cook for another minute until fragrant.

2. Stir in the diced potatoes, beef broth, smoked paprika, salt, pepper, and thyme if using. Bring the soup to a boil, then reduce the heat to a simmer. Cook until the potatoes are tender, about 15-20 minutes.

3. While the potatoes cook, melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 1-2 minutes, stirring constantly to remove the raw flour taste.

4. Slowly whisk in the milk or cream into the roux, stirring continuously until the mixture thickens and becomes smooth.

5. Pour the creamy milk mixture into the soup pot and stir well. Let it heat through for about 5 minutes to thicken the soup a bit.

6. Remove the pot from the heat. Slowly stir in the shredded cheddar cheese, mixing until the cheese is fully melted and the soup is smooth.

7. Taste and add more salt or pepper if needed. Serve the soup hot, topped with chopped green onions or chives and a dollop of sour cream if desired.