Set the oven rack to the middle position and preheat to 350ºF (177ºC).
Line two large baking sheets with parchment paper.
In a medium bowl whisk together flour, baking soda, cinnamon, baking powder, ginger, nutmeg, cloves, allspice, and salt.
In a stand mixer fitted with the paddle attachment (or hand mixer), combine butter, granulated sugar, and brown sugar on medium-high speed until light and fluffy, 2 minutes.
Add the egg and mix until combined, 30 seconds.
Scrape down the sides of the bowl and add the pumpkin puree and vanilla. Mix until combined, 30 seconds.
Gradually add the flour mixture on low speed until combined, about 30 seconds. Mix the cookie dough with a spatula to incorporate any pockets of flour.
Spoon two tablespoon-sized mounds of cookie dough onto the baking sheets. Use a spoon to spread the dough into a circle, the dough will have a sticky consistency.
Repeat with remaining cookie dough, placing them about 2 inches apart, about 12 per baking sheet.
Bake the cookies one sheet at a time until the edges and centers are set and the bottoms are golden brown, 12 to 14 minutes. If baking less than 12 cookies per sheet, reduce time to 10 to 12 minutes.
Cool on the baking sheet for 5 minutes, then transfer to a cooling rack.
Cream Cheese frosting
In a stand mixer fitted with the whisk attachment (or hand mixer), beat 4 tablespoons softened butter and powdered sugar on medium-high speed until pale and fluffy 2 minutes.
Add cream cheese, one piece at a time and mix until smooth.
Add the cinnamon and mix until incorporated.
Spread about 1 to 2 teaspoons of frosting on the top of each cookie, and then sprinkle on the pecans.
Notes
Make Ahead: Cookies and frosting can be made a day ahead and stored separately in an airtight container. Allow the frosting to warm slightly at room temperature before filling.
Homemade pumpkin spice can be used. Add 1 ¾ to 2 teaspoons of the blend to the mixture instead of the individual spices in the ingredient list.
The cookies will become cakier when stored overnight or refrigerated.