Combine milk and half & half. Freeze in ice cube tray until solid. Puree mango in a blender or food processor fitted with the metal blade. Add frozen milk cubes, rum, sugar, lime juice, and cinnamon (and vanilla if using). Process to a fluffy puree and mound into 2 or 3 stemmed glasses. Garnish with a tropical-themed swizzled stick, a lime wedge or slice of mango.