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To make the sorbet: Combine the sugar and water ina large saucepan and bring to a boil.
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Reduce the heat and simmer for 10 minutes.
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Remove from the heat and allow to cool.
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Meanwhile, combine the orange and lime juices.
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Puree the pineapple in a food processor fitted with a steel blade or blender along with the mint leaves.
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Use some of the orange juice to moisten.
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Combine with the orange-lime juice.
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Stir the pineapple mixture into the cooled syrup.
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Either freeze in an ice cream freezer or freeze in a covered bowl.
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When frozen solid, remove from the bowl and spoon into a food processor fitted with the steel blade.
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Process until fluffy; this breaks up the ice crystals and results in a smoother texture.
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To ensure this very smooth texture, repeat the process one more time after a couple of hours (this step is optional).
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Spoon into individual serving dishes, cover with plastic and then foil, and freeze.
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Or oil a loaf pan or mold and line with plastic wrap.
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Pour in the sorbet mixture, cover tightly with plastic wrap and Work quickly so that the sorbet doesn't melt, or ice crystals will form again when it freezes.
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To make the garnish and serve: Toss together the chopped pineapple and the Cointreau if you using it.
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Add the mint leaves.
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Set aside or refrigerate until ready to serve.
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Twenty minutes before serving, place the sorbet in the refrigerator to soften.
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If you froze it in the loaf pan, unmold on a platter.
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Cut slices using sharp knife.
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IF you froze it in individual molds, unmold into bowls.
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Serve, topping each serving with the garnish.
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Advance preparation: This sorbet will hold for weeks, covered tightly, in the freezer.
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The garnish can be made several hours ahead of serving time and held in a covered bowl in the refrigerator.