Heat the 4 tablespoons of butter in a heavy saucepan. Add the onions and cook until they are translucent. Add the rice and stir until it is well coated with the butter. Add the white wine, and stir continually over medium heat until it is absorbed. Start to add 1/2 cup of hot broth, stirring as it is absorbed. Continue in this manner, adding ladles full of hot broth, and stirring continuously for about 20-25 minutes or until the rice is cooked, but remains slightly firm to the teeth. Remove from the heat, add the remaining butter and the Parmesan cheese. Serve, offering additional cheese if desired.