Bring a large pot of heavily salted water to a boil over high heat. Add the pasta and cook according to the package directions or until al dente. Meanwhile, make the pesto.
Place half of the spinach and all of the pine nuts and garlic in a food processor fitted with a blade attachment. Pulse, scraping down the sides of the bowl with a rubber spatula as needed, until coarsely chopped, about 10 (1-second) pulses. Scrape down the sides of the bowl. Add the remaining spinach and pulse until coarsely chopped, about 20 (1-second) pulses, scraping down the sides of the bowl as needed.
Add the measured Parmesan, lemon zest and juice, measured salt, and measured pepper and process until combined, about 30 seconds. Scrape down the sides of the bowl.
With the motor running, slowly pour in the oil and process until a smooth paste forms, about 30 seconds; set the pesto aside in the food processor.
When the pasta is ready, reserve 1/2 cup of the cooking water, then drain the pasta and return it to the pot. Place the pot over low heat, add the pesto and 1/4 cup of the reserved cooking water, and stir to combine. Cook, stirring occasionally, until the pasta is well coated, adding more pasta water as needed to reach the desired consistency. Taste, season with additional salt and pepper as needed, and serve with Parmesan on the side.