In a medium saucepan bring the milk, rice cinnamon stick and butter to simmer over low heat. Let it simmer uncovered for 20 minutes until rice is soft. Stirring occasionally. Should be wet. If is dry add some syrup from peaches or water.
Discard cinnamon stick.
Let it cool and stir once a while to keep it wet and creamy.
Preheat oven to 350°F.
In a medium bowl whip the egg whites until stiff peak form. Set a side.
In a medium bowl mix egg yolks and sugar until light in color.
Strain peaches and cut in slices if need it. Discard syrup.
Pour egg yolk mixture into cooled rice and stir well. Fold in whipped egg whites.
Butter or spray 10 inch rounded baking dish.
Pour half rice mixture in add peaches on top and cover with rest of rice mixture.