- Peel, half and core the pears.
- Bring 1 1/2 cups water, sugar, and vanilla extract to a boil in a saucepan over high heat. Add 3 or 4 pear halves, reduce heat to medium, and simmer gently until the pears have just turned tender, about 5 minutes.
- Remove cooked pears to a warm chafing dish or metal serving dish, and continue to cook the remaining pears.
- Increase heat to medium, and boil the syrup until it has reduced to 1 cup. Stir in apricot preserves and return to a boil. Dissolve the cornstarch in 2 tablespoons of water and stir into the simmering syrup. Cook and stir until thickened and clear, about 30 seconds.
- To serve, pour the hot sauce over the pears, and sprinkle with the rum. Carefully ignite the rum tableside with the lights turned low. Let the alcohol burn out before serving.