Bring a large pot of lightly salted water to a boil. Add the pasta and cook according to the package's instructions.
While the pasta boils, choose a large bowl for serving. You'll be using this bowl to toss the pasta as well. Take the halves of your lightly smashed garlic and rub the garlic over the bottom and sides of the plate to coat it with flavor. Once the bowl is nicely coated with garlicky goodness, discard the garlic.
Add the freshly squeezed lemon juice; gradually drizzle the extra virgin olive oil into the lemon juice with a slow and steady stream while whisking. Continue to whisk until the the oil and juice have emulsified. Whisk in a pinch of salt and half of the lemon zest.
Drain the pasta when it's done and set aside. Add the cheese to the serving bowl with the oil and lemon, crack a generous amount of black pepper over the cheese, and place the hot noodles over the cheese. Carefully but thoroughly toss the pasta around the cheese and sauce with tongs until evenly coated. Add the arugula, and give the pasta one more toss.
Grate some extra cheese over the pasta before serving, as well as the remainder of the lemon zest, and some more cracked black pepper. Serve immediately.