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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.
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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.
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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.
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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.