Bring a large pot of salted water to a boil. Add pasta and cook until al dente, following package instructions. Reserve 1/2 cup of pasta water before draining. The pasta should be tender yet firm to the bite.

While the pasta cooks, heat a small skillet over medium heat. Add pine nuts and toast, stirring frequently, until golden and fragrant, about 3-4 minutes. Remove from heat to prevent burning.

In a food processor, combine basil leaves, toasted pine nuts, garlic, Parmesan cheese, lemon juice, salt, and pepper. Pulse until finely chopped, scraping down the sides as needed to ensure even blending.

With the food processor running, slowly drizzle in 1 tablespoon of olive oil. Continue processing until the mixture is smooth and emulsified, adding more oil if necessary to achieve a creamy consistency.

Transfer the pesto to a large bowl. Gradually add reserved pasta water, a tablespoon at a time, stirring until the sauce reaches a desired consistency that clings to the pasta without being too thick.

Add the cooked pasta to the bowl with the pesto. Toss gently to coat the pasta evenly, ensuring each piece is well-covered with the sauce. The aroma of fresh basil should be prominent.

If the pasta appears dry, add a splash more of the reserved pasta water, tossing again until the sauce is glossy and evenly distributed. Avoid adding too much water to prevent diluting the flavors.

Heat the remaining tablespoon of olive oil in a large skillet over medium heat. Add the pesto-coated pasta and cook for 2-3 minutes, stirring occasionally, until heated through and slightly crisped on the edges.

Taste and adjust seasoning with additional salt and pepper if needed. The flavors should be balanced, with a hint of nuttiness from the pine nuts and a fresh, herbal note from the basil.

Serve the pesto pasta immediately, garnished with extra Parmesan cheese and a drizzle of olive oil if desired. The dish should be warm, with the cheese melting slightly over the pasta.