Roll pastry out on a floured board to fit a 9-inch tart pan with removable rim.
Lay pastry in pan, easing into corners. Fold excess pastry down and flush with pan rim, then press against pan side so pastry extends about 1/8 inch above rim.
Bake in a 350° oven until pastry is lightly browned, 10 to 15 minutes. Use hot or warm.
Meanwhile, in a bowl, stir together crushed gingersnaps, brown sugar, and 2 tablespoons flour. Mix in melted butter. Squeeze mixture to form lumps. Set aside.
In a large bowl, mix granulated sugar and cornstarch. Peel, core, and thinly slice apples. Stem, peel, and thinly slice persimmons. Add fruit to bowl along with lemon juice and mix well.
Pour mixture into pastry and shake pan to settle filling evenly, then crumble gingersnap mixture over it.
Bake tart on lowest rack of a 325° oven until pastry is browned and filling bubbles, 1 hour to 1 hour and 10 minutes. Lay a sheet of foil over streusel if it begins to darken before pastry is done. Let stand until warm or at room temperature; remove pan rim.
Note: Nutritional analysis is per serving.