In a large bowl, cream shortening, white sugar and brown sugar. Beat in the egg and vanilla extract. Combine the flour, baking soda and salt; mix into the sugar mixture until well blended. Divide dough in half, cover and refrigerate for 4 hours.

To make the filling: Combine dates, sugar, water, lemon juice and salt in saucepan. Cook over low heat until mixture thickens.

Preheat oven to 350 degrees F (175 degrees C).

Roll out dough on a floured surface to a thickness of 1/8 of an inch. Cut out an even number of 2 1/2 inch circles. Place half of the dough circles 2 inches apart on cookie sheets. Brush circles lightly with water and place a tablespoonful of filling in the center of each one. Place the remaining circles on top and crimp the edges with your fingers or a fork. Make two tiny slits at the top of each cookie and brush the tops with a beaten egg. Sprinkle with sugar.

Bake 10 to 12 minutes in the preheated oven, or until lightly colored. Let cool on wire racks.