Wash green beans; trim ends, and remove strings. Cut beans into 1-inch pieces. Set aside.
Bring water to a boil in a Dutch oven. Add potato, and cook, uncovered, 2 minutes. Stir in pasta; bring to a boil, and cook, uncovered, 5 minutes. Add beans, and cook 5 additional minutes or until potato and pasta are tender. Drain and set aside.
Position knife blade in food processor bowl. Add basil and remaining 7 ingredients; process 30 seconds or until smooth, stopping once to scrape down sides.
Place pasta mixture in a large bowl; add basil mixture, and toss well.