Preheat oven to 350 degrees F. Prepare a baking sheet with parchment paper.
Halve peaches, remove pit and slice into 1/4 inch thick slices. Add sugar, cinnamon, nutmeg and salt to a medium bowl and toss peach slices in mixture.
Unfold puff pastry on a lightly floured surface. With a rolling pin, roll the pastry slightly to stretch. Cut pastry into thirds and lay each on baking sheet. Arrange peach slices on top of each third, overlapping.
Bake 20 minutes, or until pastry is golden. Remove from oven and sprinkle with chopped pecans or walnuts. Serve with whipped cream or ice cream, if desired.