1. Place mango cubes into the bowl of a food processor fitted with the S blade. Pulse to break up the pieces somewhat. Add lime juice and maple syrup, if using; blend on medium speed.
2. While the machine is running, slowly pour in the milk. Blend until completely smooth. (Be patient and don’t add any more liquid — it might not look like it’s getting there, but it will!)
3. Freeze in an airtight container. Thaw slightly before serving for a scoopable texture.
4. For an even creamier outcome (and more scoopable texture), do a double blend: Spread the sorbet in a 9×13-inch (23×33-centimeter) pan and freeze for one and 1/2 hours. Remove from freezer, cut into cubes, and blend again until creamy. Transfer to an airtight container and freeze.