Add the cooked rice, nut milk, coconut milk, maple syrup, vanilla extract, cinnamon, nutmeg and salt to a saucepan. Stir with a wooden spoon or spatula.
Place the saucepan over medium heat and bring the mixture to a simmer, stirring occasionally. Allow mixture to cook for about 10 minutes.
Add the cornstarch/ water mixture. Stir and cook for a further 5 minutes.
Remove the pot from the heat and let the pudding cool for a few minutes if serving warm. Alternatively, you can let it cool completely.
To cool the pudding, place into small jars or other dish and place in the refrigerator for 30 minutes to 1 hour.
Optional: Serve with cinnamon stick and cinnamon powder.