Cook the pasta according to package instructions. Drain in a colander and rinse it under cold water to stop it from cooking any further. Reserve about 1 cup of the pasta water.
Season the steak generously with salt and pepper on both sides.
Heat the skillet on high heat then add the butter and olive oil. Once the butter has melted and the pan is really hot, you should see wisps of smoke, add the steak and cook the first side for 5 minutes, flip over and cook for another 5 minutes. See recipe notes on cooking time.
Transfer the steak to a cutting board or plate and cover with aluminum foil. Do not slice it right away as all the juices will come out and you'll end up with a dry steak. Wait at least 5 to 10 minutes before slicing into it.
Drain the skillet and add another tbsp of butter to it. Once the butter has melted add the garlic and saute for about 30 seconds until the garlic becomes really aromatic.
Add the tomatoes, olives and capers to the skillet then season with salt and pepper. Saute for about 2 minutes until the tomatoes soften and the skins begin to wrinkle a bit.
Add the pasta, reserved pasta water, Parmesan cheese and parsley to the skillet then toss everything together.
Remove the foil from the steak and slice it across the grain using a sharp knife that will cut cleanly through the meat. Slicing across the grain will yield the most tender slices.
Place the steak slices over the pasta and serve warm.