Heat a large skillet over medium-high heat. Add beef and onion. Cook and stir until beef is browned and crumbly, 5 to 7 minutes. Drain and discard grease. Add garlic, thyme, basil, salt, and pepper. Add cream of mushroom soup, beef broth, and mushrooms. Reduce heat and simmer until flavors meld, about 20 minutes. Fold in sour cream just before serving.