Boil the pasta as directed on the package. Drain and set aside.
Heat two large skillets—one to high heat, and one to medium. The skillet over high heat is for the steak. Add the butter and 2 tablespoons oil to the skillet. Salt and pepper the steaks.
Drop the basil leaves into the hot butter and oil; flash fry for 30 seconds to 1 minute. Watch out—the fat will pop as the moisture is released from the basil. When the leaves look crispy, but still green, remove them with a slotted spoon and place them on a paper towel.
Next add the steaks to the skillet. Sear for 4 minutes per side, for medium-rare.
Remove from the pan and tent with foil. Let the steaks rest for 5-10 minutes.
Meanwhile, add 1 tablespoon of oil to the second skillet over medium heat. When the oil is hot, add the garlic, parsley, olives, capers, anchovy paste, oregano, and red pepper. Sauté for 3 minutes.
Then add the tomatoes and simmer another 5 minutes. Toss the pasta and arugula into the sauce. Toss until the pasta warms through. You shouldn’t need to salt this, because of the briny ingredients.
You can serve each person a whole steak, but for my family I usually just buy 2 large steaks and slice them on the bias. I fan them out next to the pasta. Serve the steaks drizzled with pan juices and topped with crispy basil leaves!
If your steaks are thicker than 1 1/2 inches, it can be hard to pan sear them perfectly. Preheat your oven to 450 degrees F. Then sear the first side for 4 minutes. Turn the steaks over and place the pan in the oven for about 6 minutes for medium-rare. This will ensure you don’t have a crispy outside and raw inside!Save a skillet! If you are not in a hurry, you can make both the steaks and the sauce in one skillet to reduce clean-up.