Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper. In a mixing bowl, combine the flour and half of the sugar, then add softened butter. Mix until crumbly and resembles coarse sand. Press this mixture into the bottom of the baking sheet to form a crust and bake for 10 minutes. Once baked and cooled slightly, set aside.
In a separate bowl, beat the cream cheese until smooth using an electric mixer or whisk. Add remaining sugar, sour cream, egg, and vanilla extract. Mix until well combined and the mixture is smooth and slightly thickened. This forms the cheesecake filling.
Spread the cheesecake filling evenly over the baked crust, smoothing the surface with a spatula. Bake for an additional 15 minutes until set and slightly puffed. Allow to cool to room temperature, then refrigerate for at least 1 hour for the filling to firm up.
While the cookies are cooling, prepare the strawberries by hulking and slicing them thinly. Once the cookies are cooled and set, gently fold the sliced strawberries into the cheesecake layer or arrange them on top for presentation.
Serve the cookies chilled, optionally garnished with additional sliced strawberries or a light dusting of powdered sugar to finish. The final texture features a chewy crust combined with a creamy, tangy cheesecake filling and fresh fruit.