Preheat your oven to 350°F (175°C) and line an 8x8-inch baking pan with parchment paper, allowing some overhang for easy removal later.
In a mixing bowl, cream together the softened butter and granulated sugar until fluffy.
Beat in the egg and vanilla extract until fully incorporated.
In another bowl, whisk together the flour, baking powder, cream of tartar, and salt. Gradually add the dry mixture to the wet ingredients, mixing just until combined.
Press about two-thirds of the dough into the bottom of the prepared baking pan to create an even layer; it should be thick enough to support the cheesecake layer.
In a separate bowl, beat together the softened cream cheese, powdered sugar, cinnamon, and egg yolk until smooth and creamy.
Carefully spread the cheesecake mixture over the snickerdoodle base, smoothing it out with a spatula.
Crumble the remaining snickerdoodle dough evenly over the cheesecake layer for a delicious topping.
Bake in the preheated oven for 30-35 minutes, or until the edges are lightly golden and the center is set.
Remove from the oven and let the bars cool in the pan for at least 30 minutes. Then transfer to the refrigerator to chill for at least 2 hours for easier slicing.
Once chilled, use the parchment overhang to lift the bars out of the pan. Slice into squares and serve!