Cut cheese into 12 small portions. Let rest at room temperature.
Leave skin on pears. Slice each the long way into 1/3-inch-wide planks. Use a paring knife or apple corer to punch out any seeds. (Each slice will look something like a guitar: pear profile with a hole in the belly.) Set pears on a baking sheet lined with parchment paper.
In a medium saucepan set over medium heat, whisk together butter, sugar, vanilla extract and salt until thick and foamy, about 4 minutes. Keep this caramel sauce warm over low heat.
Brush each pear plank lightly on both sides with sauce.
Spark a medium-hot fire. Clean and oil grates. (Or use a ridged griddle pan set over medium heat.) Grill pears, turning once or twice, until golden brown and nicely crisscrossed with grill marks, about 8 minutes.