This simple, sophisticated tart glistens with an apricot-Cognac glaze. Martha made this recipe on Martha Bakes, episode 505.
Preheat oven to 425 degrees, with rack in the lower third. Unfold (if necessary) puff pastry on a lightly floured surface. Working quickly, roll out dough to a 17-by-13-inch rectangle, slightly less than 1/8 inch thick. Cut off a 1-inch wide strip from each side; set aside
Transfer puff pastry to a parchment paper-lined cookie sheet. Lightly brush a 1-inch border of water around the edges of the pastry. Score strips firmly, without cutting all the way through, in a zigzag pattern with a paring knife. Lay pastry strips on edges to create a border. Trim strips to fit, overlapping at corners. Press gently to adhere. Transfer to freezer for 10 minutes.
Thinly slice pears crosswise, and brush with lemon juice to prevent browning.
Within the borders of the pastry, use the tines of a fork to poke pastry all over, to prevent it from rising. Whisk together egg and 1 tablespoon water in a small bowl. Brush borders with egg glaze. Sprinkle 3 tablespoons sugar evenly within the borders of the pastry. Top with pear slices arranging in rows, filling in any holes with chopped pears. Press gently to flatten slightly. Sprinkle pears with remaining 2 tablespoons sugar. Freeze again for 10 minutes.
Bake tart for 10 minutes. Reduce oven to 375 degrees, and continue to bake until crust is puffed and deep golden brown and pears are tender, about 1 hour. If dough under pears begins to rise, use the tip of a paring knife to allow any air to escape. Transfer tart to a wire rack, and let cool completely.
Heat jelly with Cognac in a small saucepan until melted, stirring until smooth. Brush over pears. Serve the tart at room temperature.