IMPORTANT TIP: For best results make the caramel in a stainless steel skillet or saucepan. You should be able to see how dark the caramel is before removing from the heat. If using a saucepan, transfer the finished caramel to a 9-inch ovenproof pan or skillet before adding the pears and pastry. Baking in a cast iron skillet works well, as long as you make the caramel in a light-colored saucepan first.
Pour the sugar and water into a 9-inch stainless steel ovenproof skillet. Stir to combine. Bring to a boil over medium-high heat. Once the mixture comes to a boil, reduce the heat to medium and carefully swirl the pan occasionally until the it is medium-dark amber-brown in color, but not too dark! This happens quickly so don’t walk away.
Remove from the heat then quickly and carefully add the butter and cinnamon. Stir until blended. Set aside. The caramel should be thick at this point.
Peel, quarter and core the pears. Arrange the pear slices in concentric circles, cut sides up, over the caramel until the skillet is full.
Return the skillet to the stovetop over medium-low heat and cook for about 20 to 30 minutes. The pears will release their juice and thin the caramel. Continue cooking until most of the extra liquid evaporates. Watch carefully and reduce the heat to low if needed to prevent the caramel from burning.
While the pears are cooking preheat the oven to 375°F. Line a rimmed baking sheet with foil and set aside.
Roll out the pastry to a 10-inch circle on a lightly floured, clean work surface.
Remove the pears from the heat and carefully place the pastry over the skillet. Using a large spoon or spatula tuck the edges of the pastry down into the skillet around the pears. Place the skillet on the prepared baking sheet and bake until the crust is golden brown, about 25 to 30 minutes.
Cool the tart on a rack for 20 minutes. Loosen the pastry from the sides of the pan using a wooden spoon or spatula. Place a rimmed serving platter over the tart and carefully and quickly invert the skillet. Slice into wedges and serve.