In a large pot of boiling, salted water, cook the linguine according to package instructions. Drain; return to the pot.
Meanwhile, in a large skillet, heat 1 tbsp. EVOO over medium-low heat. Add the garlic and cook until golden, 5 minutes; transfer to a cutting board and finely chop.
Season the steaks with salt. Increase the heat to medium-high, add the steaks and cook, turning once, for 5 minutes for medium-rare; transfer to a broiler-safe pan and reserve the skillet.
Preheat the broiler. Return the skillet to medium-high heat. Add the tomatoes, their juices and the garlic; season with salt and pepper. Cook, stirring occasionally, until slightly thickened, about 5 minutes. Pour the sauce over the steaks and top with the mozzarella. Broil until the cheese is melted and browned in spots, about 3 minutes.
Place the pasta pot over the medium heat and add the remaining 2 tbsp. EVOO, the parmesan and arugula. Cook until the arugula is wilted; season with salt and pepper. Serve the steaks with the pasta.