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1.
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Peel the ginger and cut into 1/4-inch-thick disks.
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2.
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In a deep saucepan large enough to hold the pear halves in a single layer, combine the ginger, sugar, and 1/2 cup of the water.
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Bring to a boil over high heat.
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Cook the syrup until it turns a medium amber brown.
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Remove the pan from heat and carefully add the remaining 2 1/2 cups water.
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Stir until the caramel is completely dissolved.
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Add the vanilla bean to the syrup.
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3.
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Peel the pears, leaving the stems intact.
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Cut the pears in half lengthwise.
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Use a melon baller to remove the central core.
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Draw the melon baller from the core to the top of the pear, removing the interior stem, up to the top of the pear.
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Add the pears to the caramel syrup.
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4.
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Simmer and cook the pears, uncovered, until they are tender but not mushy when pierced with a sharp knife, 15 to 20 minutes (the length of poaching time depends on the ripeness of the fruit).
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Stir in the pear brandy, if using.
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5.
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Remove the pan from heat and let the pears cool to room temperature in the poaching liquid.
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The pears can be served immediately, or covered and refrigerated in the poaching liquid for up to 2 days.
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6.
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To serve, drain the pears and place each pear half on a dessert plate.
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Place a scoop of vanilla ice cream alongside or on top of the poached pear.
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Drizzle with chocolate or caramel sauce.
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Sprinkle with the pistachios and serve immediately.