Preheat your oven to 350°F (175°C). Grease and flour a round cake pan or line it with parchment paper for easy removal.
In a large mixing bowl, cream together the softened butter, granulated sugar, and light brown sugar until the mixture is light and fluffy. This can be done with an electric mixer on medium speed for about 3-5 minutes.
Add the whole egg and egg yolk to the creamed mixture one at a time, mixing well after each addition. Stir in the vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, cream of tartar, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix, as this can affect the texture of the cake.
Transfer the cookie cake batter to the prepared pan, spreading it evenly.
In a small bowl, mix a tablespoon of granulated sugar with a teaspoon of ground cinnamon. Sprinkle this mixture evenly over the top of the cookie cake batter.
Place the pan in the preheated oven and bake for approximately 25-30 minutes, or until the edges are golden brown and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Allow the Snickerdoodle Cookie Cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
Once the cake has cooled, slice it into wedges or squares. Serve and enjoy your delicious Snickerdoodle Cookie Cake!