Preheat the oven to 350℉ and line a baking sheet with parchment paper and set aside
On a plate lined with paper towels, add the pumpkin puree. Press the water out with a paper towel over top and repeat until there's barely any liquid coming out. This may take 5 passes with new sheets of paper towels.
In a microwave safe bowl, melt the butter in the microwave until just melted. Add to a large bowl for mixing and let cool for 10-15 minutes
In a separate bowl, add the following dry ingredients: flour, baking powder, baking soda and salt, stir to combine
In the bowl of the semi-cooled butter, add the granulated white sugar, brown sugar, vanilla extract, and pumpkin puree. Mix to combine using a hand or stand mixer. Then, add in the egg and egg yolk and mix.
Add the dry ingredients into the bowl with the wet and mix until a dough forms
Use a cookie scoop to drop 6 cookies onto the prepared baking sheet. Add a cheesecake disk to the center and fold the dough gently around the cookie dough being sure to cover the cheesecake on all sides so nothing oozes out while baking
Roll the cookie round into a bowl with granulated sugar and pumpkin pie spice and place on the baking sheet
Pop in the oven and bake for 14 -16 minutes. The edges should be golden brown
While the first 6 cookies bake, make the next 6 on another baking sheet and pop in the oven once the first batch is done. Repeat until all the dough has been used.
Wait for cookies to cool and enjoy!