Combine the milk, mint, and sugar in a medium saucepan and bring to a boil over medium heat, stirring until the sugar has completely dissolved, about 10 minutes. Remove from the heat, cover partially with a lid, and let the milk infuse with the mint for 20 minutes.
Pour the mint milk into a blender and blend until uniform. Let it cool for 10 to 15 minutes, then pour the liquid into a freezer-safe container or baking pan.
Place in the freezer until solid and cover the container to store.
When ready to serve, let the ice milk sit at room temperature for about 10 minutes, then scrape with a large spoon. It will be slightly slushy, but not as slushy as a granita.