Prepare an ice bath in a large bowl filled with ice water.
Bring a small saucepan of lightly salted water to a boil. Add peas and cook for 2 minutes. Drain peas and add them to the ice bath, then drain again.
Set aside ½ cup of your cooked peas.
In a food processor, whirl the remaining cup of peas with garlic, pine nuts, ⅓ cup parmesan, and salt until smooth, about 2 to 3 minutes. Scrape down the bowl as necessary.
With the machine running, drizzle in olive oil.
Cook linguine until al dente. Reserve about two cups of pasta cooking water, then drain linguine and return it to the pot.
Over moderate heat, toss pasta with pesto, reserved peas, and as much reserved pasta water as needed to smooth and distribute pesto. Let cook for one minute.
Adjust salt to taste, add freshly ground black pepper if desired.
Serve immediately, garnished with fresh herbs and remaining parmesan for passing.
