Preheat oven to 325 F.
In a large bowl beat the eggs and sugar together.
Pour in the almond milk and coconut milk and mix well.
Add the vanilla, cinnamon, and rice. Stir.
Pour mixture into a 2 ½ quart casserole dish.
Bake uncovered for 60 minutes.
After 60 minutes take the dish out of the oven, stir well.
Return stirred pudding to the oven and bake an additional 30-45 minutes. (While pudding is baking make the Spiced Apple Compote)
The rice pudding is ready when it has started to thicken.
Serve warm on its own or sprinkled with nutmeg and topped with Spiced Peach Compote.