In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, and pumpkin spice; Set aside.
In a separate large bowl, beat together the butter and sugars on medium high-speed until fluffy, about 2 minutes.
Beat in puree, egg and then add vanilla. Slowly add dry ingredients on low-speed just until combined. Cover and chill dough for an hour or overnight in the refrigerator.
To make the cream cheese filling: beat cream cheese, sugar and vanilla together. Chill for 30-60 minutes.
Preheat oven to 350 and line your baking sheets with parchment paper. In a small bowl, combine the sugar and spices for the coating and set aside.
To make the cookies: take a tablespoon of the cookie batter. Flatten it like a pancake and place a teaspoon of the cream cheese in center. Form another tablespoon of the cookie batter into a flat pancake shape and place on top of the cream cheese. Pinch the edges together sealing in the cream cheese and roll into a ball. Roll in the cinnamon sugar-coating and place on the prepared baking sheet, 2 inches apart.
Repeat until the dough is gone and flatten the cookie dough balls with a heavy bottomed glass or measuring cup.
Bake the cookies for 10-15 minutes or until the tops start to crack. Let cool on the baking sheet for 5 minutes and transfer to a wire rack. Cookies will stay fresh in an airtight container on countertop for up to 5 days.