Special equipment: A food processor, an ice cream maker, optional
If using, prepare the bowl of the ice cream maker according to manufacturer's directions.
Place the mango chunks in the food processor and puree until smooth. You should have about 3 cups of puree. Place the 3 cups of puree in a mixing bowl and stir in the simple syrup, lime juice, and chili powder. Pour the mixture into a shallow dish and place in the freezer. Freeze for at least 3 hours and up to overnight.
If using an ice cream maker, pour into maker and freeze according to manufacturers directions. Transfer the sorbet to a freezable container and freeze until firm, about 1 to 2 hours.
Serve cold, sprinkled with a little coarse salt and more chili powder, if desired.
In a small saucepan, dissolve the sugar in the water and bring to a boil. Boil 2 to 3 minutes, then remove from the heat and allow to cool completely.