4 tablespoons butter, divided
1 lb pound lean ground beef
¾ cup chopped onion
¾ cup shredded carrots
¾ cup chopped celery
1 teaspoon dried basil
1 teaspoon dried parsley
4 cups cubed potatoes
3 cups chicken broth
¼ cup all-purpose flour
1 ½ cups whole milk
2 cups cubed Cheddar cheese
¼ cup sour cream
Melt 1 tablespoon butter in a large pot over medium heat; add ground beef, onion, carrots, and celery. Cook and stir until beef is browned and crumbly, 5 to 7 minutes.
Stir in basil and parsley. Add potatoes and broth and bring to a boil; reduce heat to low and simmer until potatoes are tender, 10 to12 minutes.
Melt remaining 3 tablespoons butter in a small saucepan over medium heat. Add flour and whisk until smooth, about 1 minute. Gradually whisk in milk; simmer and stir until sauce is thick and smooth.
Stir sauce into soup, stirring constantly. Bring to a boil; reduce heat to low and stir in cheese until melted. Add sour cream; stir until just heated through.
Close up view of cheeseburger soup with cheese and green onions in a bowl with a spoonful of soup