Sauté the carrot and onion cubes in the hot oil until the onions are translucent. Then add the rice rubbed with a cloth. Let this also turn glassy while stirring. Pour in the hot broth and cook covered for about 20 minutes over low heat. Add the peas and ham and cook for another 10 minutes. Then fold in the butter and parmesan cheese.
You may need to add more broth during the cooking time, but this should be completely absorbed by the rice.