Cook potatoes in a large pot of boiling water 5 minutes or just until tender.
Remove potatoes with a slotted spoon; place in a large bowl.
Add green beans to boiling water, and cook 3 minutes or until crisp-tender.
Remove green beans with a slotted spoon; place in bowl with potatoes.
Add pasta to boiling water, and cook 9 minutes or until pasta is done.
While vegetables and pasta cook, combine 2 tablespoons Parmesan cheese and next 3 ingredients in a food processor or blender. With processor on, slowly pour oil through food chute; process until well blended.
Drain pasta, reserving 1/3 cup cooking liquid.
Add pasta to bowl with potatoes and green beans.
Sprinkle with salt and pepper.
Add reserved 1/3 cup cooking liquid to food processor; process until well blended.
Add pesto to pasta mixture; toss gently to coat. Spoon pasta into individual bowls, and sprinkle with remaining 2 tablespoons cheese.