Bring a pot of salted water to a boil and cook the pasta until just al dente, saving about a cup and a half of the starchy cooking water before draining. While the pasta cooks, warm freshly ground black pepper in a heavy pan over medium heat until it becomes fragrant and slightly smoky, then pour in about three-quarters of a cup of the reserved pasta water to create a base. Add the drained pasta to the pan and, over low heat, work in the Pecorino cheese a little at a time, tossing quickly and adding splashes of pasta water as needed until the sauce turns glossy and creamy, coating each strand. Once the pasta is silky, toss in shaved lemon zest to bring a fresh, bright lift to the richness. Serve immediately in warm bowls, finished with extra Pecorino, a few more cracks of pepper, and, if desired, a light drizzle of olive oil.