Take the spinach out of the freezer for at least 1 hour before cooking. Bring a pot of salted water to a boil. Add the rice and cook for 15 minutes. Add the spinach and cook for 10 minutes more. Drain the rice and the spinach in a colander, pressing out as much liquid as possible. They should not be overcooked.
Place the spinach and rice in a heavy-bottomed pan and add the milk. Cook over low heat and, stirring rapidly, add the cheese and eggs. Add the nutmeg, salt, and pepper. After 4 or 5 minutes, add the olive oil and blend well. Serve with a bowl of grated cheese on the side.
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