1. Peel the ginger and cut into 1/4-inch-thick disks.
2. 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. Bring to a boil over high heat. Cook the syrup until it turns a medium amber brown. Remove the pan from heat and carefully add the remaining 2 1/2 cups water. Stir until the caramel is completely dissolved. Add the vanilla bean to the syrup.
3. Peel the pears, leaving the stems intact. Cut the pears in half lengthwise. Use a melon baller to remove the central core. Draw the melon baller from the core to the top of the pear, removing the interior stem, up to the top of the pear. Add the pears to the caramel syrup.
4. 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). Stir in the pear brandy, if using.
5. Remove the pan from heat and let the pears cool to room temperature in the poaching liquid. The pears can be served immediately, or covered and refrigerated in the poaching liquid for up to 2 days.
6. To serve, drain the pears and place each pear half on a dessert plate. Place a scoop of vanilla ice cream alongside or on top of the poached pear. Drizzle with chocolate or caramel sauce. Sprinkle with the pistachios and serve immediately.
Courtesy of Simple French Desserts by Jill O'Connor (Chronicle Books, 2000)