In a bowl, weigh or measure the white and light brown sugars, set aside. In another bowl, weigh or measure the flour, salt, baking powder, and allspice (run a whisk through) set this bowl aside. In a stand or hand-held mixer, add the sugars, butter, cream cheese, and cream until all three are blended, about 3 or 4 minutes on medium speed.
Mix in the egg yolk, vanilla extract, and pumpkin puree till blended. Turn the mixer down and slowly add the flour mixture. After the flour is incorporated, I scrape down the sides and turn the mixer on for another 10 to 20 seconds. Cover the bowl lightly with plastic wrap and refrigerate for 30 minutes.
I use a small scoop, but you can certainly use a medium; you do not get as many cookies per batch. Place 12 scoops onto a parchment-lined cookie pan, and I use my fingers to flatten down the tops, so it is easier for you to put the icing on after they cool. Bake at 350° for 10 - 12 minutes and move to a cooling rack before frosting the cookie tops. I made 4-½ dozen using the small scoop.
Add the cream cheese, vanilla extract, butter, and cream together. Turn the mixer to low and slowly add the powdered sugar blend until there are no more lumps. Spread a nice amount on top of each cookie.