In a large pan cook the sugar and water over medium heat for 5 minutes until dissolved. Keep an eye on it and shake pan so sugar swirls, stir often until a deep amber.
Meanwhile take puff pastry from refrigerator and thaw on counter.
Core and slice 8 slices per apple.
When the caramel is a deep amber color remove from heat add vinegar and butter. Be careful as it may splatter. Stir to incorporate completely.
Arrange apples cut side down in a single layer in pan. Cook for 10-15 minutes. Continue to place any leftover apple slice in the carmel pan as room permits.
Next roll out your puff pastry dough. Flour your board and roll out to an 11" square. Round out edges with a knife, prick holes all over with a fork and slide onto a cookie sheet, cover to not dry out and set aside until ready to use.
Next, remove pan from heat and set on heat proof area. Place the puff pastry on top of the pan and tuck the edges around the apples to completely cover. Place on center rack of oven for 30 minutes.
Let cool for 5 minutes and get ready to flip on to a plate. Be careful this is tricky. If any apples stick, don't worry you can slip them in after. With hand mits on, place your plate on top of the hot pan. Grip the sides of both and turn over. Lift the pan slowly and if you see any stuck apples gently slide a rubber spatula under to remove and place in the Tarte Tartin on the plate.
Scrape the remaining carmel on top and immediately place the pan under hot water to start dissolving and clean after.
After a few times doing this you will be a pro, don't worry - you can do this!