Position racks in the upper and lower thirds of the oven;preheat oven to 375 degrees. Line two baking sheets with parchment paper and lightly spray with nonstick cooking spray, set aside.

Whisk flour, baking powder, baking soda, cinnamon, allspice, and salt together in a medium bowl. Whisk brown sugar, pumpkin, oil, egg, and 1/2 tsp vanilla together in a large bowl. Add the flour mixture to the pumpkin mixture and stir with a wooden spoon until just combined.

Drop tablespoonfuls of dough 2 inches apart on the prepared baking sheets. Bake for 6-8 minutes, then remove from oven and with the back of a teaspoon or using your thumb, make an indentation in the center of the cookie. Return pans to oven, switching the placement of the pans and continue baking for another 4-6 minutes. Let cool for 5 minutes before removing to a wire rack to finish cooling completely.

To make the filling: beat the cream cheese and butter in a bowl on medium-high speed until smooth. Add the powdered sugar, lemon juice and remaining vanilla; beat until incorporated. Transfer to a pastry bag fitted with a small round tip; pipe into the indentions and dust with cinnamon.