Heat oil in a large skillet over medium-high heat. Add beef and sear until browned on all sides, 5 to 7 minutes. Stir in garlic and cook until fragrant, about 1 minute.
Add undrained mushrooms, tomato sauce, red wine, salt, and pepper. Simmer until beef is tender, about 30 minutes, adding a little more wine if desired. An instant-read thermometer inserted into the beef should read 140 degrees F (60 degrees C) for medium.
