In a large bowl, combine tapioca pearls, coconut milk, shredded coconut and sugar . Place milk, butter and vanilla essence in a medium saucepan and bring to the boil.
Add hot mixture to the bowl and stir to combine. Cover with aluminum foil and set aside for 40 minutes.
In a separate bowl, combine sweetened condensed milk and eggs. Add to tapioca mixture. Set aside.
Preheat your oven to 350F/ 180C
Start making your caramel. In a medium saucepan, add sugar, water and cream of tartar. Cook over medium heat, stirring constantly, until sugar is dissolved, about 2-3 minutes. Increase heat to medium-high, and boil, without stirring, for about 10 minutes, until caramel turns a light amber brown color,
Remove from heat and quickly pour the caramel in your molds/ ramekins to cover the bottom. Be careful, the pan will get very hot, so you will need pot holders!
Carefully spoon over the pudding mixture. Transfer baking dishes to a roasting pan and add enough boiling water to pan to come halfway up sides of baking dish. Cover pan with foil and bake for 40 minutes. Chill for 15 minutes.
To serve, invert baking dish onto a plate. Garnish with chopped Brazil nuts.