Bring a large pot of heavily salted water to boiling. Add rigatoni and cook according to package directions until al dente, usually 12-13 minutes. One minute before draining, reserve ½ cup pasta water. Drain pasta in colander but do not rinse.

While pasta cooks, remove steak from refrigerator and pat completely dry with paper towels on both sides. Season both sides generously with Cajun seasoning, kosher salt, and black pepper, pressing spices into the meat. Let sit while you heat the pan.

Heat a large skillet over medium-high heat for 2-3 minutes until very hot. Add olive oil and 1 tablespoon butter, swirling to coat. When butter stops foaming, carefully lay steak in pan. Sear without moving for 3-4 minutes until deep brown crust forms. Flip and sear other side 3-4 minutes for medium-rare (130-135°F internal temperature). Transfer to cutting board, tent loosely with foil, and rest for at least 5 minutes.

Reduce heat under skillet to medium. Add remaining 2 tablespoons butter and let melt. Add minced garlic and sauté for 30 seconds, stirring constantly, until fragrant and just barely golden.

Pour beef broth into skillet, scraping bottom to release browned bits. Simmer for 1 minute to reduce slightly. Add heavy cream and bring to gentle simmer. Cook for 2-3 minutes, stirring occasionally, until sauce begins to thicken.

Reduce heat to low. Add shredded mozzarella and grated Parmesan, whisking constantly as cheese melts to prevent clumping. If sauce seems too thick, add reserved pasta water a few tablespoons at a time, whisking until desired consistency is reached.

Add drained rigatoni to skillet with sauce. Using tongs or large spoons, toss pasta thoroughly for 1-2 minutes until every tube is completely coated. If pasta looks dry, add more pasta water one tablespoon at a time.

Slice rested steak against the grain into thin strips, about ¼-inch thick. Divide creamy rigatoni among four serving plates. Arrange steak slices on top. Sprinkle with red pepper flakes if using, scatter fresh parsley over everything, and finish with a small squeeze of lemon juice. Serve immediately.