1. Preheat oven to 350 degrees.
2. Cream butter and sugars together until light and fluffy, about 3-4 minutes.
3. Mix in egg and vanilla extract.
4. With the mixer on low speed, add flour, cornstarch, baking soda, dry pudding mix and cocoa powder.
5. Stir in chocolate chips. Add milk, if needed. Dough will be thick.
6. Make balls of about 1 tbsp and then flatten a bit into thick discs and place on cookie sheet. They will spread a little while they bake.
7. Bake for about 7-8 minutes.
8. Remove from oven and allow to cool for 2-3 minutes on cookie sheet, then transfer to cooling rack to cool completely.
9. While cookies cool, make icing. Beat the shortening and butter until smooth.
10. Slowly add 3 cups of powdered sugar. Mix until combined.
11. Mix in the pumpkin puree and pumpkin pie spice.
12. Add the rest of the powdered sugar and mix until smooth. Add more water until it’s the right consistency.
13. Once cookies are cool, make cookie sandwiches.
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