In a large soup pot or Dutch oven, brown and crumble ground beef until no longer pink. Drain and remove beef to a separate plate. Set aside.
Wipe pot, if needed. Melt butter in pot over medium heat and then add onions and carrots. Sauté until tender, about 8-10 minutes.
To the pot, add potatoes, chicken broth, basil, oregano, paprika, parsley, salt and pepper.
Stir and bring mixture to a boil, then reduce heat, cover, and simmer until potatoes are tender, about 10 minutes.
Add ground beef, milk (start with one cup and add more, if needed), and sour cream. Stir and adjust seasonings, if needed. Remove from heat and stir in shredded cheese until melted.