Place all the ingredients in a food processor and blend until smooth, about 2 minutes.
Line a rimmed baking sheet with parchment paper so that the paper hangs over the edge on all four sides if possible. (You'll need a pan that can sit flat in your freezer.) Pour the puree into the pan, then use a spatula to spread it evenly.
Freeze the puree until solid, about two hours. The texture will be firm but not hard like ice.
Break the frozen puree into pieces. Place them in a food processor and blend for about 5 minutes to form a smooth, creamy sorbet, pausing as needed to push down and break up the pieces with a wooden spoon. You may need to work in batches.
Serve the sorbet immediately, or for a firmer texture, place it in a metal bowl and return it to the freezer for 30 minutes.
Use the puree to make tasty popsicles. Simply pour it into molds and let it freeze until solid, about 3 hours.