Bring the water, milk, rice, and cinnamon stick to a boil in a large saucepan over medium heat. Bring to a boil, uncovered, stirring occasionally until the water is almost absorbed, 10 minutes.
Stir in coconut milk, sugar, vanilla bean seeds and bean, almond extract, butter, and salt. Bring to a boil over medium heat.
Reduce heat to medium-low and cook rice uncovered, stirring often until the mixture has thickened to almost a pudding-like consistency, 20 minutes. Remove from heat add the egg yolk. Mix well and transfer to a large bowl.