Place a large pot of water over high heat and bring up to a boil to cook the pasta. Once at a boil, add some salt and the pasta and cook until al dente, according to package directions. Drain pasta thoroughly and cool.
While the pasta is working, add the toasted pistachios, basil, mint, parsley, garlic, salt and ground black pepper to a food processor. Pulse until finely chopped. Stream in 1/2 cup EVOO, pulse until combined, transfer into a large mixing bowl and stir in the Parmigiano Reggiano. Reserve.