Preheat the oven to 350°F (175°C). Line your pan with parchment, leaving overhang for easy lifting.
Make the cookie base: Beat butter and sugar until light and fluffy, about 2 minutes.
Mix in the egg and vanilla.
Whisk flour, cream of tartar, baking soda, and salt. Add to the butter mixture and mix just until combined.
Press about two-thirds of the dough evenly into the pan. Reserve the rest for topping.
Make the cheesecake: Beat cream cheese until smooth.
Add sugar and mix until creamy. Beat in eggs one at a time, then vanilla and sour cream.
Pour the cheesecake batter over the cookie base and spread evenly.
Pinch off small pieces of the remaining cookie dough and scatter over the top. It won’t fully cover—gaps are good.
Stir together cinnamon and sugar.
Sprinkle evenly over the top, covering both cheesecake and dough pieces.
Bake 28–34 minutes (8x8 pan), until the edges are set and the center has a slight wobble. Don’t overbake.
Cool completely on a rack, then chill at least 3 hours (overnight is best). Slice into squares with a sharp knife, wiping between cuts.