Preheat the oven to 325°F. Grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared pan to form the crust.
In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add 1 cup sugar and vanilla extract, mixing until well combined.
Add the eggs one at a time, mixing well after each addition.
In a separate bowl, whisk together the sour cream, flour, cocoa powder, red food coloring, vinegar, and baking soda until smooth.
Gradually add the sour cream mixture to the cream cheese mixture, blending until fully incorporated.
Pour the cheesecake batter over the crust in the springform pan.
Bake in the preheated oven for 50-60 minutes, or until the center is set but slightly jiggly. Turn off the oven and leave the cheesecake inside for an additional hour.
Remove the cheesecake from the oven and let it cool to room temperature. Refrigerate for at least 4 hours or overnight before serving.