Bring a small saucepan of lightly salted water to a boil. Add peas and cook for 2 minutes. Drain peas then add to an ice bath for about one minute to stop cooking and drain again. In a sauté pan over medium heat add a tablespoon of Garlic Olive Oil. Add tomatoes and sauté for one minute.
Set aside 1/2 cup peas. Add the remaining cup of peas in the work bowl of a food processor with garlic, 2 tablespoons pine nuts, 1/3 cup parmesan, lemon juice and salt. Process until smooth, about 2 to 3 minutes, scraping down the bowl as necessary. With the processor running, drizzle in NOOC garlic olive oil.
Cook Bucatini until al dente. Reserve about one cup pasta water then drain bucatini and return it to pot. Over moderate heat, toss pasta with pesto, cherry tomatoes, reserved peas and one cup pasta water to smooth and distribute pesto; let cook for one minute so that the pesto adheres. Adjust salt to taste, add freshly ground black pepper if desired. Garnished each plate with fresh mint, 2 tablespoons toasted pine nuts and crispy prosciutto.