Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Add the pears, cherries, sugar and cornstarch to a large saucepot and mix to coat the fruit. Add the red wine, star anise and salt. Place the saucepot over direct heat, bring the mixture to a boil and cook, simmering, until the wine is reduced and slightly thickened, about 5 minutes.
Remove the saucepot from the heat and add the red wine vinegar. Discard the star anise. Let cool slightly.
Serve by spooning over some vanilla bean ice cream.
(Alternatively, you can poach the fruit over medium-high heat on a stovetop.)