Brown the ground beef in a pot over medium heat, then add chopped onion and garlic and cook until softened for better flavor development.
Add diced potatoes and chicken broth, bring to a boil, then simmer until potatoes are tender but still hold their shape.
Prepare a roux by melting butter, whisking in flour, and slowly adding milk until smooth and thickened.
Stir the roux into the soup along with cream, allowing the mixture to gently simmer and thicken evenly.
Reduce heat and add shredded cheese gradually, stirring until fully melted and smooth.
Season the soup, let it rest briefly, then serve with desired toppings for best texture and flavor.
