Beat 2 tablespoons milk with egg yolk in a small bowl. Set aside.
Combine 2 3/4 cups milk and coconut milk in a saucepan over medium heat. When mixture just begins to steam, reduce heat to low.
Melt butter in a saucepan over medium heat. Stir in rice and cook for 1 minute. Pour in 1/2 cup coconut milk mixture; stir constantly until liquid is completely absorbed and rice is creamy. Repeat this process until the milk mixture is completely incorporated and the rice has a tender, yet slightly firm consistency, 20 to 30 minutes.
Stir sugar and salt into the rice mixture. Remove from heat. Slowly whisk in egg yolk mixture until completely incorporated and the mixture is custard color, about 1 minute. Whisk in vanilla.
Cool pudding to room temperature, cover with plastic wrap, and refrigerate until well-chilled, at least 3 hours. Garnish with mango and Chinese five-spice powder.