Toss the apples, sugar, cinnamon, allspice, and salt together in a large bowl.
Roll the pastry, on a lightly floured surface, into a 12-inch round. Line a baking sheet with parchment paper and spray with cooking spray. Arrange the pastry on the baking sheet. Put the apple mixture in the center of the pastry and spread evenly to the edges, but leaving enough dough to fold over to create a crust on the rim. Brush the crust with melted butter and drizzle the remaining butter over the apples.
Bake until the crust is golden brown, about 40 minutes.
While tart is cooking, put the peach preserves into a microwavable bowl and microwave until syrupy, about 20 seconds.
Remove the tart from oven and brush with the warmed preserves. Pull the parchment paper off the sheet tray and transfer the tart to a wire rack to cool. Cut as desired and serve.