Heat a small nonstick skillet over medium heat. Add the pine nuts and shake the pan occasionally, until they begin to brown and give off a nutty aroma, about 2 to 3 minutes. Set aside to cool.
BASIL PESTO: Combine the toasted pine nuts and basil in a food processor, pulse a few times. Add the garlic, pulse a few times more.
Slowly add the olive oil in a constant stream while the food processor is on. Stop to scrape down the sides of the food processor with a rubber spatula. Add the lemon juice and grated cheese and pulse again until blended. Add a pinch of salt and freshly ground black pepper to taste.
PASTA: Fill a large pot with water and bring to a boil. Add 1 tablespoon of salt and cook the pasta until al dente. Reserve 1/2 cup of the pasta water and drain the pasta in a colander.
Place the pesto into a large bowl. Add the hot pasta to the bowl, gently toss with tongs to combine. Add some of the reserved pasta water, if needed.
Pour into a serving bowl or individual bowls, garnish with pine nuts and Parmesan cheese; serve immediately.