Place the potatoes in a large steamer basket fitted over a pot of boiling water. Cover and steam for 5 minutes. Add the green beans to the potatoes in the steamer and continue to cook, covered, for another 4 minutes. Drain and immediately plunge into an ice bath to cool.
Transfer the vegetables to a large serving bowl. Add the pesto and stir to coat evenly. Season with salt and pepper and serve.
Make a big batch of this pesto in the summer when the basil is fresh and plentiful. You can freeze it in ice cube trays, bag up the cubes, and have it year-round to use as a pasta sauce or to enhance the flavor of one. It is also excellent as a sandwich spread.
Toast the pine nuts in a small, dry skillet over medium heat until fragrant and golden brown, shaking the pan frequently, about 3 minutes.
In a food processor, process the pine nuts and garlic together until minced. Add the basil, Parmesan, lemon juice, and salt and pepper and process until finely minced. With the machine running, slowly pour the oil in a steady stream through the feed tube and process until well blended.