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Dice the pineapple, reserving the juice.
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Measure out 1/2 cup plus 2 tablespoons of juice from the pineapple can. *Add water if it falls short.
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Heat the liquid with the sugar until the sugar dissolves.
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Add pineapple to the syrup.
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Continue simmering for about 1 minute.
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Remove from the heat and let cool.
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Squeeze limes.
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Peel and dice the mango and banana.
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Puree the mango, banana, lime juice, and maple syrup.
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Stir in the cooled pineapple syrup.
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Transfer to a freezer-proof bowl and freeze for 1 hour, stirring occasionally.
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Beat the egg whites until stiff peaks form, then fold them into the mixture.
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After about 3 hours, carefully fold in the raspberries.
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Freeze overnight, stirring occasionally.
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Scoop and serve.