On a shallow plate, grate the garlic and mix it with the EVOO. Place steaks in the oil, flipping them around a few times, the cover and marinate for at least 30 minutes.
Heat a large, cast-iron skillet over medium-high heat. Shake excess oil from the steak, season both sides with salt and pepper, and cook until desired doneness, about 4 minutes on each side for medium rare. Remove from the skillet and let rest for about 5 minutes.
While the meat is resting, make the gravy: Add a little of the reserved garlic and oil marinade to the skillet then stir in the flour and cook 1 minute. Whisk the balsamic and beef stock into the flour mixture, season with salt and ground black pepper and cook until thickened.