Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, melted butter, and granulated sugar, stirring until well blended. Press this mixture firmly into the bottom of a 9-inch springform pan to create a sturdy base. Bake for 10 minutes, or until the crust is lightly golden and fragrant, then set aside to cool.

In another mixing bowl, beat softened cream cheese and sour cream together with an electric mixer until completely smooth, free of lumps. Gradually incorporate granulated sugar, mixing well before adding eggs one at a time, ensuring each is blended thoroughly. Stir in the vanilla extract, crafting a dreamy, creamy filling.

Divide the cheesecake filling in half. Add green food coloring to one half, adjusting the color until you achieve your desired vibrancy. In the springform pan atop the cooled crust, alternate spoonfuls of the plain and colored fillings, using a knife or skewer to gently swirl them together.

Carefully transfer the pan to your preheated oven, baking for 55-60 minutes until the center is set but still slightly jiggly. Turn off the oven, crack the door open, and allow the cheesecake to cool slowly for 30 minutes.

Place plastic wrap over the cheesecake and refrigerate for at least 4 hours or ideally overnight.

When ready to serve, carefully remove the cheesecake from the springform pan. Garnish with fresh mint leaves or grated chocolate shavings.