Preheat your oven to 350°F (175°C). Lightly grease a 9-inch pizza pan or line it with parchment paper. Press the sugar cookie dough evenly over the bottom of the pan to form a crust.

Bake for 12-15 minutes, or until the edges are lightly golden brown and the center is set. Remove from the oven and let cool completely on a wire rack. This is crucial; you don't want to add the filling to a warm crust!

While the crust cools, beat the softened cream cheese in a medium bowl with an electric mixer until smooth and creamy. Gradually add the powdered sugar, then mix in the vanilla extract and milk (or heavy cream) until the mixture is light, fluffy, and completely combined. Scrape down the sides of the bowl as needed.

In a small saucepan, combine the raspberries, granulated sugar, and lemon juice. Bring to a gentle simmer over medium heat, stirring occasionally, and cook for about 3-5 minutes until the raspberries start to break down and release their juices.

In a small separate bowl, whisk together the cornstarch and cold water until smooth. Pour this cornstarch slurry into the simmering raspberries, stirring constantly. Cook for another 1-2 minutes, until the topping has thickened to a jam-like consistency. Remove from heat and let cool completely; it will thicken further as it cools.

Once the cookie crust and raspberry topping are both completely cool, spread the cheesecake filling evenly over the cookie crust. Then, carefully spoon the cooled raspberry topping over the cheesecake layer, spreading it gently to the edges.

Refrigerate the raspberry cheesecake pizza for at least 1-2 hours, or preferably longer, to allow the cheesecake filling to set properly. This will make slicing much easier and cleaner.

Just before serving, dust lightly with extra powdered sugar and garnish with fresh mint leaves, if desired. Slice into wedges and enjoy!