Cream shortening and sugar until light and fluffy.
Add eggs, one at a time, beating well after each addition. Beat in vanilla.
Mix the pumpkin and milk together, in a separate container, and set aside.
In another bowl, whisk together the flour, baking powder, baking soda, salt and pumpkin pie spice. Beat into creamed mixture alternately with pumpkin milk mixture.
Set batter aside to rest for 30 minutes.
Preheat the oven to 350 degrees, and line three baking sheets with parchment paper.
Drop by heaping tablespoonfuls (I like to use a cookie scoop) onto parchment=-lined baking sheets, about two inches apart. Flatten slightly with the back of a spoon.* Bake 12-14 minutes, or until they spring back when lightly touched.
Leave the cakes on the baking sheet, and place the baking sheet on a rack to cool.
When cookies are completely cooled, spread filling on half of the bottoms, and top with the remaining half of the cookies. Cover individually in plastic wrap, and store at room temperature for two to three days -- or in the refrigerator.
Notes
*Pro Tip - lightly spray or rub the back of your spoon with oil before flattening the cakes.