Put the rice, water and cinnamon sticks in a medium pot over medium-high heat.
Bring to a boil, uncovered, reduce the heat to medium low and cook until the rice is tender, about 25 minutes. Discard the cinnamon sticks.
Stir in the whole milk, evaporated milk, salt, vanilla, sugar, arequipe. Continue cooking over medium heat about 10 minutes more, stirring often.
Reduce the heat to low and cook, uncovered, stirring constantly, until the mixture is thick, about 20 minutes.
Transfer the rice pudding to a serving bowl. Drizzle the top of the pudding with arequipe or dulce de leche and serve.