Beef Preparation: Begin by cooking the ground beef in a large saucepan over medium heat until fully browned, about 6-8 minutes. Once done, drain the beef and set it aside.
Vegetable Sauté: Continue in the same pan by melting 1 tablespoon of butter. Add in the onion, carrots, celery, basil, and parsley, sautéing until these vegetables soften, roughly 10 minutes.
Combine Ingredients: Now introduce the potatoes, chicken broth, and previously cooked beef to the pan. Allow the mixture to reach a boil, then simmer with a cover until the potatoes are soft, about 10-12 minutes.
Roux Creation: While the soup simmers, melt the remaining butter in a different small skillet and whisk in the flour until the mixture bubbles and thickens, which should take about 3-5 minutes.
Thicken Soup: Add this flour mixture to your simmering soup, bringing it to a boil while stirring for another 2 minutes until thickened.
Cheese and Seasoning: Lower the heat and blend in the cheese, milk, salt, and pepper, stirring until the cheese is completely melted into the soup.
Sour Cream Mix-In: Once off the heat, stir in the sour cream for a creamy texture. Serve with optional garnishes such as onion rings and green onions for added flavor and crunch.