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1.
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In a medium saucepan, combine the sugar, water, the 3 cinnamon sticks, the peppercorns and cloves and bring to a boil over moderately high heat.
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Remove from the heat and let infuse for 5 minutes.
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2.
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Add the pears to the spice syrup and bring to a simmer over moderate heat.
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Reduce the heat and simmer until the pears are just tender, about 15 minutes.
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Pour into a large bowl and let cool.
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3.
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When the pears are cool enough to handle, remove them from the syrup and cut into 1/2-inch cubes.
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Strain the syrup and add enough water to measure 6 cups.
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Pour the syrup back into the saucepan and bring back to a simmer.
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4.
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In a large pot, melt 1 1/2 tablespoons of the butter over moderately low heat.
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Add the rice and cook, stirring, for 1 minute.
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Add 1 cup of the simmering syrup, the rum and the salt.
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Cook, stirring constantly, until the syrup has been completely absorbed.
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The rice and syrup should bubble gently; adjust the heat as needed.
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Continue cooking the rice, adding the syrup 1 cup at a time and allowing the rice to completely absorb the syrup before adding the next cup.
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Cook the rice in this way until it is tender, about 45 minutes in all.
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The syrup should thicken from the starch in the rice.
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You may not need to use all of the liquid, or you may need to use more depending on the rice.
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If you need more, just add simmering water.
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Stir in the remaining 1 1/2 tablespoons butter.
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5.
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Stir the pears into the risotto and spoon into shallow bowls.
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Top each serving with a scoop of the ice cream and, if using, a mint sprig and a cinnamon stick.