Preheat the oven to 325°F. Line an 8x8-inch baking dish with parchment paper, leaving some overhang for easy removal.
In a medium bowl, combine the chocolate graham cracker crumbs and melted butter. Mix until the crumbs are evenly coated. Press the mixture firmly into the bottom of the prepared baking dish to form the crust. Bake for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Add the granulated sugar, vanilla extract, and egg. Mix until well combined and creamy.
Gently fold in the raspberries and cornstarch until evenly distributed.
Pour the cheesecake mixture over the cooled crust, spreading it evenly. Bake for 25-30 minutes, or until the edges are set and the center is slightly jiggly.
Remove from the oven and let cool at room temperature for about 30 minutes, then refrigerate for at least 2 hours to set.
Once chilled, lift the cheesecake out of the baking dish using the parchment paper. Cut into bite-sized squares and serve.