Combine jasmine rice and water in a saucepan, bring to a boil. Lower the heat, cover and simmer until the rice is tender and the water is absorbed, about 25 minutes.
Add 1cup of coconut milk and sugar; simmer for 10~12 minutes or until the rice is completely tender and pudding like.
Stir in the orange zest, nutmeg and the remaining ¼cup of coconut milk. Let the jasmine rice pudding cool to room temperature.