First, remove the moisture from the pumpkin puree. Spread the pumpkin puree in a thin layer on several layers of paper towels. Use additional paper towels to blot the pumpkin puree until most of the moisture is removed and the pumpkin puree is dry. The pumpkin puree will reduce by half, so you should have ⅓ cup of pumpkin puree remaining. Set aside.
In a medium mixing bowl, whisk together the all-purpose flour, pumpkin pie spice, baking soda, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, mix together the melted unsalted butter, light brown sugar, and granulated sugar until well combined. Add in the dried pumpkin puree, egg, egg yolk, and vanilla extract, and mix until combined and smooth. Add in the flour mixture and mix on low speed until the cookie dough forms.
Portion the pumpkin cookie dough using a large cookie scoop (3 tablespoons). While the cookie dough is in the cookie scoop, press a frozen cheesecake ball into the center of the cookie and wrap the cookie dough around the cheesecake filling. Roll the cookie dough to form a smooth cookie dough ball. Place the cookie dough balls on a parchment-lined baking sheet pan and chill in the refrigerator for 30 minutes.
Preheat the oven to 350℉ (177℃). Line baking sheet pans with silicone baking mats or parchment paper.
In a small bowl, stir the granulated sugar and cinnamon together. Roll the chilled cookie dough balls in the cinnamon sugar to coat.
Place the cookie dough balls on the prepared baking sheet pans, allowing room for spreading. Bake the cookies for 12 to 14 minutes until the edges are set. Cool the cookies on the pan for 2 minutes and then transfer to a wire rack to cool completely.