Preheat oven to 400 degrees. On a lightly floured surface, roll the puff pastry into a large rectangle approximately 1/8 inch thick. Sprinkle a baking sheet with a little water. Transfer pastry to prepared baking sheet, and place in the refrigerator to chill, 30 minutes.
Core the apples and slice them crosswise on a mandoline as thinly as possible, about 1/16 inch thick. Remove chilled pastry from refrigerator. Sprinkle with 1 tablespoon sugar. Spread applesauce evenly over pastry. Place apple slices on the pastry in overlapping rows to cover, leaving a 1-inch margin around the edge. Sprinkle with remaining 3 tablespoons sugar. Brush the edges with heavy cream. Bake until the edges are golden brown, about 35 minutes.
Heat apple jelly in a small saucepan over medium-low heat until melted. Brush the apples with the jelly to glaze.