Mix 1/3 cup coconut, brown sugar, rum, melted butter and 1/4 of the pineapple juice together in a bowl. Pour into the bottom of a 2 1/2-quart casserole dish. Place bread cubes on top.
Mix coconut milk beverage, orange juice, white sugar, eggs, remaining coconut, remaining pineapple juice, cinnamon, and nutmeg together in large bowl.
Pour over bread cubes and sprinkle with a little cinnamon.Bake in the preheated oven for 60 minutes or until a knife inserted in the center comes out clean.
Place a large bowl in an ice bath and set aside. In a small bowl, combine egg yolks, cornstarch, 2 tablespoons milk and brown sugar and stir until smooth.
Combine 1 cup milk, white sugar and vanilla in a small saucepan and bring to a boil.
Whisk the yolk mixture into the boiling milk. Immediately pour the sauce from the pan into the bowl sitting in the ice bath to prevent curdling.
Add rum and whisk thoroughly. Serve warm over the bread pudding.