Preheat oven to 375 degrees and spray a 24 cup mini muffin tin with cooking spray.
In the bowl of a stand mixer with the paddle attachment or with a handheld mixer, beat together the softened butter, pumpkin puree, brown sugar, and granulated sugar for about 3 minutes on medium high speed.
Scrape down the side of the bowl and add in the egg and vanilla extract.
Beat the mixture for another minute.
In a separate bowl whisk together the flour, spices, baking soda, and salt.
Pour the dry ingredients into the wet and beat on medium low speed just until combined.
Fold in the mini chocolate chips with a rubber spatula.
Using a small cookie scoop (2 teaspoon size), scoop the dough into the mini muffin tin.
Bake in the oven for approximately 7-9 minutes or until done.
Remove from the oven and use the back of a spoon or measuring spoon to press down the middle of the cookie cup forming a small crater.
Remove the cookie cups from the muffin tin and place them on to a wire cooling rack to cool completely before frosting them.
Pumpkin Cream Cheese Frosting:
In the bowl of a stand mixer with the whisk attachment or with a handheld mixer, whisk together all of the ingredients for the pumpkin cream cheese frosting until they are fluffy and smooth.
Cover and chill the frosting for about 30 minutes to help it set up so it is easier to pipe or spoon into the cookie cups.
Pipe or spoon some of the frosting into each of the cooled cookie cups and top with more mini chocolate chips if desired.
Chilling the frosting is optional, but I find that it is easier to pipe when it is cold.