Bring 3 cups of water to a boil in a medium pot over medium heat. Stir in the rice, cover, turn to low and let simmer until the rice has absorbed all the water and is tender, about 20 minutes. (You can also cook the rice in a rice cooker.)
In a large saucepan over low heat, combine the coconut milk, sugar, vanilla, salt and orange zest and cook until the mixture is hot and the sugar is dissolved, 4 to 5 minutes; do not let the mixture boil or the coconut milk could curdle. Stir in the cooked rice, cover and cook on low until thick and the rice has absorbed most of the coconut milk, for an additional 15 to 20 minutes.
To serve, scoop the rice pudding into individual bowls, top with diced mango and garnish with mint sprigs.