Steak: Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a small baking sheet with vegetable oil cooking spray. Set aside. Season the steaks with salt and pepper, to taste. In a large skillet, heat the oil over medium-high heat. Add the steaks and brown on all sides, about 4 minutes. Transfer to the prepared baking sheet and bake for 10 minutes for medium-rare doneness. Let the steaks rest for 5 minutes on a cutting board.
Gravy: In the same skillet used for the steak, heat 2 tablespoons of oil over medium-high heat. Add the shallots and mushrooms and season with salt and pepper, to taste. Cook until the shallots are soft, about 5 minutes. Add the wine and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Cook until most of the liquid has evaporated, about 2 minutes. Stir in the beef broth and rosemary. Whisk in the flour until smooth. Bring the mixture to a boil. Reduce the heat to a simmer and cook, stirring occasionally, until half of the liquid has evaporated and the sauce has thickened slightly, about 10 minutes. Remove the pan from the heat and stir in the butter until smooth. Season with salt and pepper, to taste.
Cutting across the grain, slice the steak into 1/4-inch thick slices and arrange on a platter. Pour the sauce into a serving bowl and serve alongside the meat.