Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente; drain in a colander and rinse briefly under cold water to stop cooking. Reserve about 1 cup of the pasta cooking water.
Season the ribeye steak generously on both sides with 1/2 teaspoon salt and 1/2 teaspoon black pepper.
Heat a 12-inch cast iron skillet over high heat until very hot. Add 1 tablespoon butter and 1 tablespoon olive oil; when the butter melts and the pan begins to smoke slightly, add the steak.
Sear the steak 5 minutes on the first side, flip and cook about 5 minutes more for medium-rare (adjust time for thickness or desired doneness). Transfer the steak to a cutting board, tent with foil, and rest 5–10 minutes before slicing.
Discard any excess fat from the skillet, then add the remaining 1 tablespoon butter. When melted, add the minced garlic and sauté about 30 seconds until aromatic.
Add the cherry tomatoes, Kalamata olives and capers to the skillet. Season with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper, and sauté about 2 minutes until the tomatoes begin to soften and wrinkle.
Add the cooked pasta, reserved pasta water, grated Parmesan and chopped parsley to the skillet; toss gently until the cheese melts and the sauce coats the pasta, adding more pasta water as needed for desired consistency.
Slice the rested steak across the grain into thin slices and arrange over the pasta. Serve warm.