Add the rice and water to a pot and heat it on medium-high heat. Once it reaches a boil, turn the heat down to low and simmer for 10 minutes.
Add the evaporated oat milk, sugar, vegan butter, salt, orange peel, cinnamon stick, and seeds scraped out from a vanilla bean to the pot. Heat it on medium-high heat.
Once the mixture reaches a boil, reduce the heat down to low and simmer for 30 minutes while stirring often to avoid the rice from sticking to the pot.
Take the pot off the heat, pour the mixture into a heat-safe bowl, and let it cool.
If serving the rice pudding cold, cover the bowl making sure the plastic wrap touches the surface of the rice pudding and put the bowl in the refrigerator to chill for about an hour.
While the rice pudding chills, make the orange compote. Cut the oranges and grapefruit into segments and put them into a heatproof bowl.
In a pot, add the sugar, water, maple syrup or agave, any juice collected while cutting the citrus, cinnamon stick, and the vanilla bean pod leftover from making the rice pudding. Heat it on medium-high.
Once it reaches a boil, turn the heat down to low and simmer for 10 minutes. Pour the liquid over the oranges and let it cool completely.
Serve with the rice pudding.