Preheat your oven to 325°F. Grease a 9-inch springform pan.
In a medium bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan to form the crust.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add 1 cup of sugar and continue to beat until creamy.
Add the vanilla extract, eggs (one at a time), and sour cream, mixing well after each addition.
In a small bowl, mix the cocoa powder, red food coloring, vinegar, and baking soda to create a smooth paste. Add this mixture to the cream cheese batter and mix until fully incorporated and the color is uniform.
Pour the cheesecake batter over the crust in the springform pan.
Bake in the preheated oven for 50-60 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside for an additional hour to cool gradually.
Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours, preferably overnight, before serving.