Preheat your oven to 325°F (160°C). In a medium mixing bowl, combine the graham cracker crumbs and 1/4 cup of granulated sugar, mixing well. Pour in the melted butter and stir until the mixture is evenly moistened. Firmly press this mixture into the bottom of a 9-inch springform pan to form a solid crust. Bake the crust in the preheated oven for 10 minutes. Once baked, remove it from the oven and allow it to cool slightly.
In a large bowl, use an electric mixer on medium speed to beat the softened cream cheese and 1 cup of granulated sugar together until the mixture is smooth and creamy. Next, add the eggs one by one, ensuring to mix thoroughly after each addition to maintain a consistent texture.
To the cream cheese mixture, incorporate the sour cream, fresh lemon juice, and lemon zest until well blended. Gently fold in the fresh raspberries and raspberry purée, being careful not to break the raspberries too much, as you want to maintain their shape.
Sprinkle the tablespoon of cornstarch over the cheesecake mixture. Gently fold it in, which will help stabilize the cheesecake and contribute to its desired creamy consistency.
Pour the cheesecake filling over the prepared crust in the springform pan. Bake in the oven for 50-60 minutes, or until the edges are set, while the center remains slightly jiggly. Once baked, turn off the oven and leave the cheesecake inside with the door ajar for 1 hour, allowing it to cool gradually.
After the hour has passed, remove the cheesecake from the oven and let it cool to room temperature on the counter. Once it has cooled, cover it with plastic wrap and refrigerate for at least 4 hours, but for optimal flavor, overnight is best.
When ready to serve, run a butter knife around the edges of the springform pan to loosen the cheesecake. Carefully remove the sides of the pan. For a beautiful presentation, garnish the top of the cheesecake with additional fresh raspberries and a drizzle of raspberry purée.
Notes
For optimal flavor, refrigerate overnight before serving.