Once the filling is frozen, Line a cookie sheet with parchment paper and set aside.
Mix the flour, salt, cornstarch, baking powder and pumpkin pie spice in a medium bowl. Set aside.
In a separate, large mixing bowl, beat together the melted butter, granulated sugar and dark brown sugar, using an electric hand mixer, until light and fluffy. Make sure there are no lumps in your brown sugar!
Add in the egg and vanilla extract and beat again until well combined.
Add the flour mixture into the butter mixture and mix until it forms a wet dough. **
Take the filling dots out from the freezer.*** and mix together the remaining granulated sugar and pumpkin pie spice in a small plate.
Drop the cookie dough onto the cookie sheet in 1 Tbsp-sized balls. Break each ball in half and place a cheesecake dot in the center, and then roll the cookie dough around it. **** Roll the whole ball in the sugar mixture and place on the cookie sheet, just flattening slightly. You want the cookies taller than they are wide, so they are big and soft! Repeat until all the cookies are done. Place into the freezer for 2 hours.
Once the cookies have been frozen, preheat your oven to 350 degrees and stick them immediately into the oven.
Bake for 10-12 minutes, until the outsides feel just set. The cookies will feel very soft and under baked, but they firm up a lot once cooled!
Let them cool for 10 minutes on the cookie sheet and then transfer to a wire rack to finish cooling.
We also really liked these with browned butter, as they have a nuttier taste this way. To brown butter just melt it in a sauce pan over medium heat, stirring frequently until it turns a light golden brown. It goes from brown to burnt fast, so watch it closely!
*If your use the butter immediately after melting, and it is hot, your dough me a little too stick to form into balls right away. If this happens, just stick it in the fridge for 20 mins before stuffing with the cheesecake centers!
*** I recommend taking only half out at a time, so they don't melt while you are rolling the cookies!
**** You will have a couple left over cheesecake dots. Aw shucks ;)