Heat the water and stock to boiling in a medium saucepan. Add the rice and cook covered over very low heat until all the liquid is absorbed, 15 to 20 minutes. The rice should be a little wet and sticky. Stir in the egg and Parmesan. Season to taste with salt, pepper, and nutmeg. Spread the mixture on a baking sheet and cool in the refrigerator.
Roll the rice mixture into