Cook the ground beef in a 3-quart saucepan until browned, then drain off the excess fat and set the beef aside. The meat should lose its raw pink color and leave browned bits in the pan, while draining keeps the finished soup from getting a greasy layer on top.

Add 1 tablespoon of butter to the same saucepan, then cook the onion, carrots, celery, parsley flakes, and basil until the vegetables soften. You should smell the butter and herbs bloom, and the onion should look translucent rather than sharply white.

Pour in the chicken broth, add the potatoes and browned beef, and bring the pot to a boil before lowering the heat and covering it to simmer for 10 to 12 minutes. The potatoes are ready when a fork slides in easily with little resistance and the broth smells rich and savory.

Meanwhile, melt the remaining 3 tablespoons of butter in a small skillet, stir in the flour, and cook it for 3 to 5 minutes until bubbly before adding it to the soup; bring the soup back to a boil, stir for 2 minutes, then reduce the heat to low. The roux should look lightly golden and smell toasty instead of raw, with gentle bubbling that shows the flour has cooked through.

Stir in the cheese, milk, salt, and pepper over low heat until the cheese melts, then remove the pot from the heat and blend in the sour cream. The soup should look creamy and unified, with no boil and no grainy curds once the dairy is fully incorporated.