Preheat your oven to 325°F (163°C).

In a mixing bowl, combine the graham cracker crumbs, melted butter, and sugar. Mix until well combined.

Press the graham cracker mixture firmly into the bottom of a 9-inch springform pan to form an even crust. Bake for 10 minutes, then let cool.

In a large mixing bowl, use an electric mixer to beat the cream cheese until smooth and creamy. Gradually add the granulated sugar and mix until well combined.

Add the eggs one at a time, mixing well after each addition. Then, mix in the vanilla extract, cocoa powder, and red food coloring until evenly combined.

Finally, add the sour cream and mix until the batter is smooth and creamy.

Pour the red velvet cheesecake filling into the cooled crust and smooth the top with a rubber spatula.

Bake the cheesecake for approximately 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and leave the cheesecake inside for an additional 30 minutes.

Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours, preferably overnight.

To prepare the cream cheese frosting, beat the softened cream cheese and butter together until smooth. Gradually add the powdered sugar, mixing until well combined.

Add the vanilla extract and mix until incorporated. If needed, add milk for desired consistency.

Once the cheesecake is chilled, remove it from the springform pan. Spread the cream cheese frosting evenly over the top.

Slice and serve chilled. Enjoy your red velvet cheesecake!