Add the milk, rice, cinnamon stick, and citrus peels to a large pot.

Bring to a gentle simmer over medium heat for 40 minutes, making sure it doesn't boil vigorously.

Stir continuously; the more you stir, the more starch the rice releases, giving the pudding a creamier texture.

When the pudding reaches your desired texture, remove the peels and cinnamon stick, add the sugar, and cook for another 10 minutes.

Remove from heat, let it rest for 1 minute, then stir in the butter until melted.