Apple–Puff Pastry Pyramids with Almond Ice Cream and Caramel Sauce

This variation of the French classic mille-feuille is the result of an effort to utilize the crumbs and trimmings inevitably produced whenever a sheet of baked puff pastry is cut into strips to make Napoleons or any of that dessert’s hybrids. One way to minimize the scraps and also speed up the assembly is to use what I call the production method for making Napoleons. Here, three full sheets of baked puff pastry are layered with the filling, glazed, trimmed, then cut into four length