01 - Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 1/2 cup pasta cooking water, then drain.
02 - While the pasta cooks, prepare the pesto: In a food processor, combine the peas, mint, basil, Parmesan, pine nuts, garlic, salt, and pepper. Pulse until finely chopped.
03 - With the motor running, drizzle in the olive oil and lemon juice. Process until smooth, scraping down sides as needed. If the pesto is too thick, blend in a little reserved pasta water.
04 - Return the drained pasta to the pot. Add the pesto and toss to coat, using reserved pasta water as needed to loosen the sauce.
05 - Fold in the extra fresh peas if using, lemon zest, and half of the remaining Parmesan.
06 - Divide among plates. Top with additional Parmesan and black pepper to taste. Serve immediately.