Add the milk and sugar to a pot and heat to dissolve the sugar. Stop before it comes to a boil.
Prepare ice water in a large bowl. Cool the pot of sweetened milk from Step 1 in it. Once the mixture cooled, pour into an ice cube tray and freeze for 1 day.
Add sugar and water to the shiratamako and knead. Roll into bite-sized balls. Boil the balls to soften (until about as soft as your earlobes). Once they start to float to the top, transfer them to a bath of ice water.
Discard the juice from the mango can, add the mangoes to a blender and mix smoothly. Add sugar and the mangoes to a pot and heat for about 2 minutes.
Once Step 4 cools, add the orange juice and chill in the refrigerator.
Take the ice cubes from Step 2 and use an ice shaver to make shaved ice. Top with the mango sauce, condensed milk, and ice cream in that order.
Top with the shiratama dumplings, frozen mangoes, and it's complete!!