Coconut Brown Rice Pudding

1. In a medium saucepan bring rice, coconut milk, and milk just to a boil on medium-high. Reduce temperature to medium-low and keep to a low boil. Let boil and thicken for 50 minutes, stirring occasionally. Stir more at the end as the mixture gets thicker.
2. Meanwhile, put the flaked coconut into a dry pan over medium heat to toast. When a small amount of toasted bits show up (about 5 minutes), turn off burner, but keep the pan on it, stirring to finish toasting with the burner off.
3. Add the sugar and cinnamon to the rice mixture and stir. Cook for 5 minutes. Beat the egg in a bowl and temper by adding small amounts of the rice mixture to the egg while stirring until the egg feels warm, then add the egg mixture to the rice mixture while stirring. Cook for 2 minutes.
4. Transfer to a bowl or individual serving bowls. Refrigerate until cold and top with toasted coconut just before serving.