Preheat the oven: Set your oven to 350°F (175°C) and lightly grease an 8×8-inch baking dish with non-stick spray or line it with parchment paper for easy removal.
Make the cheesecake filling: In a medium bowl, combine softened cream cheese, egg, and vanilla extract. Beat with an electric mixer on low speed until smooth and creamy. If you prefer a sweeter filling, add a tablespoon or two of powdered sugar and mix again until well blended.
Form the crust: Cut the sugar cookie dough in half. Press one half evenly into the bottom of the prepared baking dish to create the crust.
Add the cheesecake layer: Pour the cream cheese mixture over the sugar cookie base and spread it evenly to cover the surface.
Top with cookie dough: Break the remaining sugar cookie dough into small chunks, flatten them slightly, and scatter evenly over the cheesecake layer. These pieces will spread during baking to form a golden, slightly crackled top.
Bake: Bake for 30 minutes, or until the top is lightly golden and set. Keep an eye on it near the end to prevent over-browning.
Cool and finish: Remove from the oven and allow to cool in the pan for at least 1 hour. For a firmer texture, refrigerate for an additional 30 minutes. Add sprinkles on top for a fun, festive touch.
Serve: Slice into squares and enjoy at room temperature or chilled.