Fill a large pot with water, generously adding salt to enhance the flavor, and bring it to a rolling boil over high heat. Add 400 grams of spaghetti or linguine and cook until al dente, which should take about 8-10 minutes. Reserve one cup of the starchy pasta cooking water before draining.

While the pasta cooks, zest the two large lemons into a mixing bowl, then squeeze their juice into the same bowl. Add three tablespoons of extra virgin olive oil and whisk gently until well combined.

Finely grate one cup of Parmigiano Reggiano cheese and add it to the lemon mixture. Stir gently to incorporate and create a creamy consistency.

Carefully transfer the hot, drained pasta to the bowl with the creamy lemon mixture. Toss the pasta with the sauce, ensuring each strand is well-coated. Gradually add reserved pasta water until achieving the desired creaminess.

Continue mixing until the sauce coats the pasta evenly. Season with freshly ground black pepper and salt to taste. Serve immediately, garnished with extra cheese if desired.