Stand one of the mangos upright with the narrow end facing you. Slice off the 'cheeks' on either side of the stone and slice these in half lengthwise. Cut around the stone to take off as much flesh as possible, capturing all the running juices in a bowl.
Remove the skin by peeling or cutting the fruit carefully off it. Repeat with the other mango. Discard the skin and puree the flesh and juice in a food processor or blender.
Add the milk and sugar, and combine until it becomes a thick smooth mass. Transfer the liquid to a pitcher and chill the mixture until ready to drink. Add the ice cubes to the pitcher and serve straight from the refrigerator. A little goes a long way, so serve in small glasses.