Preheat oven to 350 degrees F (190 degrees C). Line baking sheets with parchment paper.
Cream the butter or margarine with the sugar. Beat in the pumpkin, egg and vanilla.
Stir the flour, baking soda, baking powder, salt and ground cinnamon into the pumpkin mixture. Blend until combined.
Drop teaspoonfuls of dough onto the prepared baking sheets. Bake at 350 degrees F (175 degrees C) for 12 to 14 minutes. Let cookies cool completely then sandwich two cookies together with Vanilla Filling.
To Make Vanilla Filling: Beat the shortening and 1 1/2 cups white sugar together for 10 minutes. Beat in the vanilla and the vanilla pudding. Beat until creamy.