Place potatoes in a large saucepan; add water to cover. Bring to a boil. Reduce heat; cook, uncovered, until tender, 8-10 minutes. Drain; transfer to a large bowl., Meanwhile, cook pasta according to package directions, adding green beans during the last 5 minutes of cooking. Drain, reserving 3/4 cup pasta water; add to potatoes. Toss with pesto, cheese and enough pasta water to moisten.