Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper.
Combine melted butter, egg and sugars in a large bowl or bowl of your stand mixer fitted with the paddle attachment. Mix vigorously for about 1 minute. Add pumpkin pie filling, molasses, cinnamon, nutmeg, ginger, allspice, baking soda and salt. Mix for another minute to combine.
Using a sturdy spatula or wooden spoon, fold flour into wet mixture. Using a small ice cream scoop, drop dough onto prepared baking sheets. Bake for 10 minutes, or until tops of cookies spring back lightly when touched.
For Frosting:
Once cookies are completely cooled, combine softened cream cheese and powdered sugar in a large bowl. Beat well to combine until smooth. If desired, add a little milk or cream to thin frosting. Frost cookies.