Generously season the steak on all sides with salt and pepper. Heat 1 tablespoon of olive oil in a large skillet over medium-high heat until shimmering. Add the steak and sear without moving for 4-5 minutes per side for medium-rare, or until desired doneness. In the last minute, add the butter to the pan and baste the steak. Transfer steak to a cutting board, tent with foil, and let rest for 10 minutes.
While the steak rests, bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy pasta water.
In the same skillet used for the steak (do not wipe it out), heat the remaining 1 tablespoon of olive oil over medium heat. Add the minced garlic and cook for 1-2 minutes until fragrant but not browned. Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese until melted and smooth.
Add the drained pasta directly to the skillet with the cream sauce. Toss to coat thoroughly, adding the reserved pasta water a little at a time until the sauce reaches a silky consistency that clings to the pasta. Stir in the fresh parsley, thyme, and lemon zest.
Slice the rested steak against the grain into thin strips. Divide the creamy garlic pasta among four bowls. Arrange the sliced steak pieces over the pasta. Spoon any accumulated steak juices from the cutting board over the top. Garnish with extra parsley and Parmesan if desired.