In a large mixing bowl, whisk the flour, cream of tartar, baking soda, spices, and salt together; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter until smooth, about 1 to 2 minutes. Add both sugars and continue beating on medium speed until smooth and creamy.
Scrape down the sides of the bowl, add the egg, and beat just until combined. Add the pumpkin puree and vanilla and continue beating. The mixture might look a little odd and curdled at this point, but this will change once you add the dry ingredients.
Add the flour mixture and beat on low until just combined, about 1 minute. Stir in the white chocolate chips. Cover dough and keep in the refrigerator while you make the cheesecake filling.
Make the Batter:
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese and sugar together until smooth and creamy. Add the egg, vanilla, and salt, beating until combined. Try not to over-mix the batter.
To Assemble:
Preheat oven to 350ºF degrees. Line an 8-inch square baking pan with parchment paper and spray with nonstick cooking spray. Make sure to leave extra overhang on the sides for easy removal.
Press 2/3 of the dough into the bottom of the baking pan, forming an even layer. Pour the cheesecake filling over the dough and spread out evenly. Take the remaining dough, press into thick discs, and place them on top of the filling. It's okay if some of the filling is still exposed.
Bake for 35-40 minutes, or until edges are golden brown and the cheesecake filling jiggles slightly when pan is shaken. Remove from the oven and allow to cool for at least 30 minutes before transferring to the fridge to chill for 2 hours.
Bars will stay fresh for up to one week stored in a plastic container or wrapped tightly with plastic wrap and kept in the refrigerator.