In a large saucepot, combine ice wine, balsamic vinegar, honey, cinnamon and cloves. Add pears. Bring to a boil and then lower and simmer until pears are tender, about 20 minutes. Remove pears with a slotted spoon.
Let poaching liquid simmer until reduced to about 1/4 cup, with a thick and syrupy consistency. Melt butter in a large saute pan over medium-high heat. Add pears and sear until caramelized. Cut the parmigiano-reggiano into rustic chunks and arrange them on a platter. Transfer the caramelized pears to the platter next to the cheese.
Drizzle everything with the reduced ice wine syrup.