Rub both sides of the steaks with salt, pepper, and savory. Heat butter and oil in a large, heavy skillet over medium-high heat; add garlic cloves and steaks. Lower heat to medium, and cook steaks 4 to 6 minutes on each side for medium rare. Transfer steaks to a cutting board. Add mushrooms to the pan, raise heat to high, and saute for 2 minutes on each side. Transfer mushrooms to a small bowl.
Discard garlic and fat from the pan. Add red wine and stock to the pan. Reduce over high heat, scraping bottom with a wooden spoon, until 1/2 cup of sauce remains. Combine with mushrooms.
Cut beef crosswise into 1/4-inch-thick slices, and serve with mushroom sauce on the side.