Cook beans in large pot of boiling salted water until just tender, about 5 minutes. Drain. Rinse beans with cold water and drain well. (Can be prepared 6 hours ahead. Let stand at room temperature.)
Melt butter with oil in heavy, large skillet over high heat. Add beans and toss until heated through, about 4 minutes. Season with salt and pepper. Add walnuts and parsley and toss. Transfer to bowl and serve.