Combine the orange peel, 2 cups water, the butter and a pinch of salt in a saucepan and bring to a boil. Add the rice and return to a boil, then reduce the heat to low and cook, shaking the pan occasionally, until the liquid is absorbed, about 15 minutes.
Bring the milk, granulated sugar, cinnamon sticks and vanilla to a low boil in another saucepan. Add the rice and simmer over medium-low heat, stirring, until the liquid is mostly absorbed, about 15 minutes. Stir in the grated orange zest and 1/4 cup mascarpone.
Transfer the rice pudding to a large bowl and let cool, then cover with plastic wrap and refrigerate until cold and set, about 2 hours.
Beat the remaining 1/4 cup mascarpone and the confectioners' sugar in a bowl. Remove the cinnamon sticks and orange peel from the pudding. Serve topped with the mascarpone and cinnamon.