Season the steaks liberally with salt and pepper. Preheat a large, cast-iron skillet or griddle over high heat. Drizzle the steaks with EVOO and cook, turning once, for 8-10 minutes for pink centers. Let the meat rest until cool enough to handle, then slice very thinly on a diagonal.
Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a cup of the pasta cooking water.