Prepare the Crust: Preheat your oven to 325°F (160°C). Mix the graham cracker crumbs, sugar, and melted butter in a bowl. Press the mixture into the bottom of a 9-inch springform pan to form an even layer. Bake for 10 minutes, then let it cool while preparing the filling.

Make the Cheesecake Filling: Beat the cream cheese with an electric mixer until smooth and creamy. Add sugar and vanilla extract and continue to mix until well combined. Add eggs one at a time, mixing on low speed after each addition. Stir in the sour cream. Pour the cheesecake batter over the cooled crust.

Prepare the Raspberry Topping: In a small saucepan, combine raspberries, sugar, and lemon juice over medium heat. Cook until the raspberries break down and the mixture becomes syrupy. Stir in the cornstarch mixture and cook for an additional 2-3 minutes until the topping thickens. Allow to cool slightly before spreading gently over the cheesecake filling.

Bake the Cheesecake: Bake in the preheated oven for 55-60 minutes, or until the center is set. Cool the cheesecake at room temperature, then refrigerate for at least 4 hours or overnight.

Serve: Carefully remove the cheesecake from the springform pan. Dust with powdered sugar and garnish with fresh raspberries. Serve with whipped cream if desired.