Cook linguine according to package directions in a large pot of salted boiling water. Reserve about 0.5 cup of pasta water before draining.
While the pasta is cooking, prepare the dressing. In a large bowl, whisk together the olive oil, lemon juice, minced garlic, and red pepper flakes (if using). Season with salt and pepper.
Add the drained linguine directly to the bowl with the dressing. Toss well to coat.
Add the fresh arugula and grated Parmesan cheese to the bowl. Toss gently until the arugula is slightly wilted and the cheese is incorporated.
If the pasta seems a bit dry, add a splash of the reserved pasta water, a tablespoon at a time, to create a light sauce. Toss again.
Serve immediately. Garnish with extra Parmesan cheese and black pepper if desired.
Notes
This is a versatile recipe that can be enjoyed as a light main course or a side dish. Feel free to add cooked shrimp or chicken for a heartier meal.