In a large saucepan, heat oil and butter over medium heat. Add onion and cook, stirring, until translucent; about 5 min. Add rice and mix well.
Meanwhile, in a small saucepan, warm chicken broth with water. Add 1 ladleful of hot broth to the rice. Stir until almost all of the liquid is absorbed. Repeat, 1 ladleful at a time, stirring and allowing the broth to be absorbed by the rice before adding more. When all the broth has been added to rice, turn off the heat before the liquid is completely absorbed.
Mix in Parmesan, walnuts and herbs. Transfer to a serving dish and serve immediately.