Bring a large pot of salted water to a full, rolling boil over high heat.
Pulse basil, garlic and pine nuts in a food processor until finely chopped. Stop and scrape down sides of bowl. With machine running, slowly pour in oil. Stop processor, add Parmesan and pulse until smooth. Season with salt and pepper. (Makes about 2/3 cup pesto.) Transfer to a bowl and cover.
Add beans to boiling water and cook until tender yet crisp, 4 to 5 minutes. Drain, rinse under cold running water, then dry thoroughly. Transfer to a bowl and cover.
Just before serving, toss beans in a large bowl with enough pesto to coat. (Cover and refrigerate any remaining pesto.) Season with additional salt and pepper, if desired. Serve at room temperature.