In food processor or blender, combine basil, parsley, pine nuts, garlic, and salt. Cover and blend until finely chopped. Gradually add the olive oil and process until well combined. Add the cheese and process with the on/off switch until just combined.
Meanwhile, in a 6 quart Dutch oven, cook the pasta according to the package, except add the potatoes and green beans during the last 5 minutes of cooking. Drain the pasta mixture well. DO NOT RINSE.
In a very large bowl, combine the cooked pasta mixture, pesto, and butter. Toss gently until the pasta and vegetables are well coated. Serve immediately.