In a saucepan, heat 1 tablespoon olive oil over medium-high heat. Add a third of the shallots and cook until softened, about 3 minutes. Add the beef broth, barley, dried mushrooms, chopped rosemary and 1/2 teaspoon pepper. Bring to a boil, lower the heat, cover and simmer until the barley is tender and the liquid is absorbed, about 50 minutes.
Meanwhile, on a plate, season the flour with 1/2 teaspoon each salt and pepper. Working in 2 batches, in a large, heavy skillet, heat the remaining 3 tablespoons olive oil over medium-high heat. Coat the steaks in the seasoned flour, shaking off any excess, and add to the skillet. Cook, turning once, until browned, 3 to 4 minutes. Transfer to a plate and tent with foil to keep warm.
Add the remaining shallots to the pan and cook, stirring frequently, until softened. Add the wine and 1/2 teaspoon each salt and pepper and bring to a boil, scraping up the browned bits. Cook until reduced by half, about 5 minutes. Lower the heat to medium-low, add the steaks and any juices and cook, turning once, for 3 minutes for medium.
Meanwhile, stir the spinach and parmesan into the barley mixture until the spinach wilts.
Slice the steak and serve over the barley pilaf. Top with the sauce and rosemary sprigs.