Add rice, water, butter and Penzey's Baking Spice to non-stick pot. Bring to a boil, cover and simmer for 15 minutes. Just until the water is completely absorbed.
In a bowl, whisk egg yolks and evaporated milk. When rice is done cooking, remove from heat and add the sweetened condensed milk, coconut milk, and another 1/2 tsp of the Penzey's Baking Spice. Stir to combine. Finally, add in the egg and evaporated milk mixture.
Return pot to stove. Simmer over low heat until mixture starts to bubble. Cook for 15-20 minutes, until at least half of milk mixture is absorbed. The pudding will continue to thicken as it cools, so it's okay if it still looks a bit soupy. If you find it getting too thick as it starts to cool, you can add some regular milk. Once off heat, add the vanilla.
Spoon Tres Leche Rice Pudding in glasses / container and allow to cool to room temperature. Cover and place in refrigerator for 1-2 hours. When ready to eat, you can top with whip cream and cinnamon, if desired.