Cook Beef: Cook 1/2 pound ground beef in a saucepan over medium heat for 6-8 minutes until no longer pink. Drain and set aside.
Sauté Vegetables: In the same pot, melt 1 tablespoon butter. Add 3/4 cup chopped onion, 3/4 cup shredded carrots, 3/4 cup diced celery, 1 teaspoon dried basil, and 1 teaspoon dried parsley flakes. Cook for 10 minutes until tender.
Add Potatoes and Broth: Add 1 3/4 pounds cubed potatoes, the cooked ground beef, and 3 cups chicken broth. Bring to a boil, then reduce heat and simmer for 12 minutes.
Make Roux: In a separate skillet, melt remaining 3 tablespoons butter. Stir in 1/4 cup flour and cook for 3-5 minutes until bubbly. Gradually add to the soup, stirring constantly. Bring to a boil and cook for 2 minutes.
Add Cheese and Milk: Reduce heat and stir in 2 to 4 cups shredded Velveeta cheese, 1 1/2 cups whole milk, 3/4 teaspoon salt, and 1/4 to 1/2 teaspoon pepper until cheese is melted.
Finish: Remove from heat and stir in 1/4 cup sour cream. Serve hot.
Tips
Cheese Substitute: Use Swiss, cheddar, or pepper jack instead of Velveeta.
Meat Substitute: Substitute ground beef with ground sirloin, round, or turkey.
Storage: Refrigerate up to 4 days in an airtight container. Not recommended for freezing due to dairy content.