How to Make It
Peel the pears. Using a melon baller, scoop out the core of each pear, starting from the bottom (leave the stem end intact).
In a Dutch oven or large pot, combine the cinnamon sticks, ginger, 2 cups of the sugar, and 8 cups water. Add the pears and bring to a boil, stirring gently to dissolve the sugar. Reduce heat, cover, and simmer gently until the pears just begin to soften, 10 to 15 minutes. Let cool in the cooking liquid (the pears will continue to cook as they cool).
Fifteen minutes before serving, make the caramel: In a medium saucepan, combine the remaining ½ cup of sugar and ½ cup water. Cook over medium heat, stirring just until the sugar has dissolved, 1 to 2 minutes.
Continue to cook, without stirring, until the syrup is a dark golden brown, 10 to 12 minutes more. Carefully add the cream (the mixture will sputter) and stir to combine. Serve the pears with the ice cream, drizzled with the caramel.