Bring the water and salt to boiling in a 4-quart Dutch oven. Add pasta; boil for 5 minutes. Add green beans. Continue boiling, uncovered, about 5 minutes more or until pasta is tender but still firm. Drain in a colander and set aside.
Cook leeks and walnuts in hot olive oil and butter in the same Dutch oven for 3 to 4 minutes or until leeks are tender and walnuts are lightly toasted. Stir in drained pasta mixture and thyme; heat through.
Transfer mixture to a serving platter. Sprinkle with cheese and pepper. Serve immediately.