Rinse the Thai black rice and soak overnight in 2 1/4 cups of water. Pour the rice and the water it was soaking in into a rice cooker and add coconut milk and sugar. Stir everything together and turn on the rice cooker. Once cooked, set aside to cool.
To make the mango dessert, combine the condensed milk, milk, and vanilla. Add a big scoop of sticky rice to 2 bowls, and top each bowl with a handful of shaved ice and diced mango. Pour the vanilla sauce over everything and top each bowl with a scoop of vanilla ice cream. You can also layer everything in a glass to make it a bit prettier.
To make the blueberry dessert, combine the ice, milk, condensed milk, and vanilla in a blender and blend until smooth. Pour the mixture into two bowls. Add a scoop of sticky rice to each bowl, a scoop of blueberry ice cream (you can substitute vanilla ice cream, if you want), and a handful of blueberries.