Preheat the oven to 350 degrees F (175 degrees C).
Heat the oil in a large skillet over medium heat. Cut the flat iron steak into individual portions if needed. Season with salt and pepper on both sides. Fry the steaks until browned on each side, 2 to 3 minutes per side. Remove from the skillet and place in an oven proof dish. Set steaks in the oven to continue cooking.
Add shallots and whole cloves of garlic to the hot skillet. Cook and stir over medium heat until shallots are starting to brown. Add mushrooms to the pan; cook and stir until they shrink some, 5 to 10 minutes.
Pour the balsamic vinegar into the pan with the mushrooms and stir to remove any bits that are stuck to the bottom of the skillet. Pour in the red wine and simmer for a few minutes over medium heat.
Return the steaks to the skillet and cook until the internal temperature reaches 135 degrees to 140 degrees F (60 degrees C), about 5 minutes if at all. Remove the whole pan from the heat and let stand until steaks reach an internal temperature of 145 degrees F (63 degrees C), or your desired degree of doneness.
