Tarte Tatin is an upside-down apple tart, a French classic whose creation is attributed to two sisters from the Loire Valley. Sugar and butter create a caramel-like coating that covers the apples, which becomes the topping when the tart is inverted. Our recipe substitutes peaches for the apples, and it's equally delicious with pears.
Bring a large pot of water to the boil. Drop the peaches in the water and cook for 2 minutes. Remove the peaches with a slotted spoon and drop them in a large bowl of ice water to stop the cooking process. When cool enough to handle, remove the skins and discard.
Cut the peaches in half through the stem end ("pole to pole"), and remove the pits. Set one half aside, and cut the remaining halves into 1-inch wide wedges.
Place the butter in an 8-inch cast iron skillet with 2-inch high sides and melt over medium heat. Add the sugar and stir continuously until a medium-brown caramel forms, 10 to 15 minutes. Remove from the heat and place the one peach half in the center of the skillet, rounded side down. Arrange a layer of peach wedges around the peach half, keeping the peaches close together and placing them rounded side down. Place the remaining peach wedges, rounded side up, in between the first layer of peaches, to make a tight circle.
Position a rack in the middle of the oven, and preheat to 400 degrees F.
Return the skillet to the stove, and cook over medium heat until the caramel and peach juices bubble thickly, 20 to 30 minutes. Don't set the heat too high or the caramel may burn. The peaches should be just tender, but not mushy.
Remove the skillet from the heat. Let cool 10 minutes, then carefully place the round of pastry atop the hot peaches, tucking the edges into the pan. If you're using puff pastry, cut three 1-inch long slits in the dough for vents.
Transfer the skillet to the oven and bake until the crust is golden and the filling thickens, 20 to 30 minutes.
Remove the pan from the oven and place on a wire rack. Cool for 10 minutes to allow the juices to set. Place a large flat plate or platter on top of the skillet. Place one hand on the bottom of the plate and quickly invert the skillet so the tart slides onto the serving dish. The tart will still be hot, so be sure to wear oven mitts for this step! If you've left the tart to cool longer than 10 minutes, it may be necessary to place the skillet over medium heat for 2 or 3 minutes to remelt the caramel for an easy release from the pan.
Cut into wedges and serve warm with a scoop of vanilla ice cream.