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1
Add the water and sugar to a small saucepan; grate the zest from the 2 limes directly into the saucepan.
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2
Bring mixture to a boil and cook, stirring occasionally, until the sugar is dissolved.
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3
Reserve 5 of the mint leaves; add the remaining mint to the saucepan, and remove from the heat.
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4
Cover and let stand for 8 minutes, then remove cover and let cool to room temperature.
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5
Once cool, strain the mixture into the container you plan to freeze the granita in, pressing firmly on the leaves to extract all the flavorful liquid.
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6
Discard mint leaves.
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7
Stir in the lime juice and rum; then finely chopped the reserved 5 mint leaves and add them as well.
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8
Place granita in the freezer; begin checking it after about 1 hour; once it begins to freeze around the edges, take a fork and stir the mixture, breaking up the frozen parts near the edges into smaller chunks and raking them toward the center.
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9
Return dish to freezer, then check mixture every 30 minutes afterward, stirring each time and breaking up any large chunks into small pieces with a fork, until you have beautiful, fine crystals.
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10
Serve in a chilled cocktail glass/martini glass.
