Line a baking sheet with parchment paper or lightly flour it.

Roll out the pastry on a lightly floured work surface to form an 11 ½ -inch (29cm) round. Transfer the pastry to the prepared baking sheet and refrigerate for at least 1 hour.

Spread the sugar evenly over the bottom of a very heavy (10 to 10.5inch;25 to 26.5cm) oven-proof skillet; a simple cast-iron skillet is perfect. Place the butter slices evenly over the sugar, then arrange the apple halves on top of the butter. Begin at the outside edge and stand the halves on their sides, facing in one direction with stem ends toward the center. Pack the apples as close together so they are held standing by pressure. Make a second circle of apple halves inside the first, packing them in on their edges as well. Place one apple half right in the center of the second circle to fill in the small space that remains. The idea is to get as many apples into the pan as possible, while keeping them nicely arranged.

Place the skillet over medium-low heat and cook the apples in the butter and sugar, uncovered, unti-0l the sugar turns golden brown; this will take at least 1 hour. Watch the apples closely to be sure they don’t stick; you may want to adjust the heat now and then, to slow down or speed up the cooking. As the sugar and butter melt and the apples give up some of their juices, baste the apples occasionally with a turkey baster. Gradually, the sugar will caramelize the apples nearly all the way through, though they will remain uncooked on top.

Preheat the oven to 425 F (220 C).

When the cooking juices are deep golden and the apples are nearly cooked through, remove the pastry from the refrigerator and quickly and carefully place it over the apples, gently tucking it down around them, simultaneously easing it toward the center so that if it shrinks on the sides there will still be enough of it to cover the apples.

Place the skillet on a baking sheet. Bake in the center of the oven until the pastry is golden, 25 to 30 minutes. Don’t be concerned if the juices bubble over; the tart will be more or less juicy, depending on the variety of apple you’ve used.

Remove the skillet from the oven. Immediately invert a serving platter with a slight lip over the skillet. Quickly but carefully invert the two so the crust is on the bottom, the apples are on top, and the juices don’t run off onto the floor. Remove the skillet. Should any apples stick to it, gently remove them and reinsert them into their rightful place in the tart.

Serve generous slices as soon as the tart has cooled slightly, but is still very warm through.