Preheat: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper or a silicone mat.
Prepare the cookies: In a medium bowl, whisk together flour, baking soda, cream of tartar, and salt. Set aside.
Cream the butter and sugar: In a large bowl, use an electric mixer to cream the butter and sugar until light and fluffy, about 2-3 minutes.
Add eggs and vanilla: Beat in the eggs one at a time, followed by the vanilla extract.
Add pumpkin puree and spice: Beat in the pumpkin puree and pumpkin pie spice.
Combine dry ingredients: Gradually mix in the dry ingredients (flour mixture) until just combined.
Chill the dough: Wrap the dough in plastic wrap and refrigerate for at least 30 minutes or up to 2 hours.
Scoop and roll: Scoop the dough into balls, about 1 1/2 tablespoons each. Roll each ball in cinnamon sugar to coat.
Bake: Place the balls onto the prepared baking sheet, leaving about 2 inches of space between each cookie. Bake for 10-12 minutes or until the edges are set and the centers are slightly soft.
Prepare the cheesecake filling: In a medium bowl, beat the cream cheese until smooth. Add the granulated sugar, eggs, and vanilla extract, and mix until well combined.
Assemble the snickerdoodles: Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Once the cookies are cool, use a cookie scoop or a spoon to create a small indentation in the center of each cookie.
Fill with cheesecake: Fill each cookie with a small dollop of cheesecake filling.
Top with snickerdoodle topping: Mix the granulated sugar and cinnamon in a small bowl. Sprinkle the mixture over the cheesecake filling.