Bring water to a boil and cook peas for 1-2 minutes, removing and dunking in an ice bath to stop cooking.
Bring water back to a boil and cook pasta to al dente, drain and reserve pasta cooking water.
In a food processor, combine 2 cups of the cooked peas, toasted pine nuts, mint leaves, lemon juice and garlic.
Stream olive oil into the food processor and continue to pulse until ingredients are combined.
In a large bowl, toss the pasta with the pea and mint pesto, and add in some of the reserved pasta water to coat (add this slowly and use between 1/4 to 1/3 cup), and finally the reserved 1/2 cup of peas.
Season with salt and pepper and top with grated parmesan cheese.
Serve hot immediately, or refrigerate for 1-2 hours to serve as a cold pasta salad.