After defrosting a sheet of puff pastry, roll on a parchment sheet and trim to about an 11” round. Place the parchment with pastry on baking sheet, cover with plastic wrap, and place in the refrigerator to chill while you cook the apples.
Evenly spread the sugar in the bottom of the heavy skillet and place the butter pieces on top.
Take the peeled and cored apple halves and stand them up on top of the butter in two rings. The empty core section will be facing the peeled back of the next apple. The apples in each ring should all be facing the same direction. Pack them in snugly.
Place the skillet over a medium high heat and cook for about 30 minutes. Adjust the heat occasionally if it is either bubbling too rapidly or not enough. With the turkey baster, occasionally draw up some of the bubbling caramel liquid and baste the apples.
Halfway through the cooking, preheat the oven to 425 ° Fahrenheit.
When the juices start to turn a deep golden color, quickly place the pastry over the hot apples and tuck the extra dough down around the edges.
Place in the preheated oven and bake for about 15 minutes or until the pastry has puffed.
Remove from the oven and immediately take a knife and run it around the edge of the pan.
Place the serving side of a plate that is about 1” larger than the pan on top of golden pastry and quickly invert everything so that the skillet is now on top and the plate is on the bottom with the tart in the middle. Carefully remove the skillet. If any of the apples stick to the pan, just scoop them off with a spoon and place them back onto the tarte.
Let cool a bit and serve warm.