Heat 2 tablespoons of oil in a heavy large frying pan over high heat. Sprinkle the steaks with salt and pepper. Cook the steaks until they are brown but still rare in the center, about 3 minutes per side. Transfer the steaks to a plate and set aside to cool completely. Add 2 more tablespoons of olive oil to the same pan. Saute the onions and carrots until the onions are translucent, about 8 minutes, with additional salt and pepper, to taste. Add the garlic and oregano, and saute for 1 minute. Add the wine and simmer for 1 minute. Add the marinara sauce and broth. Cover and simmer over medium-low heat to allow the flavors to blend, about 10 minutes. Season the sauce, to taste, with salt and pepper.

Meanwhile, trim off any fat from the steaks, then cut the steaks into bite-size pieces and set aside. Bring a large pot of salted water to a boil over high heat. Add the rigatoni and boil until it is tender but still firm to the bite, stirring often, about 10 minutes. Drain the rigatoni.

Toss the rigatoni and reserved steak pieces and any accumulated juices from the steaks with the sauce to coat. Transfer the pasta to bowls. Sprinkle with the Parmesan cheese shavings and serve.