Fresh Peaches in Puff Pastry

There are few combinations I can think of creating in my kitchen that are as natural together as fresh ripe peaches, buttery puff pastry, rich caramel sauce, and cinnamon—especially when the cinnamon flavor comes in the form of cinnamon ice cream, as it does here. Nectarines work just as well as peaches for this dessert, although you should try to avoid the larger size and, because most nectarines are clingstone, a different technique is required to remove the pits. Cut the nectarines in ha