Place the walnuts on an ungreased baking sheet. Bake at 350 degrees F (175 degrees C) for 5 to 8 minutes.
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 or margarine 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.