Preheat your oven to 350°F (175°C). In a mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar until it resembles wet sand. Press firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes until golden brown and cool while preparing the filling.

In a large mixing bowl, beat the softened cream cheese and sour cream until smooth and creamy. Gradually add the granulated sugar, mixing on low. Incorporate the eggs, one at a time, and finally add the vanilla extract.

Divide the cheesecake filling in half. In one half, mix in the green food coloring until vivid. Alternate spoonfuls of both mixtures in the pan, gently swirling together with a butter knife.

Bake for 55-60 minutes until set around edges but slightly jiggly in the center. Turn off the oven and leave the cheesecake to cool inside for 30 minutes with the door ajar.

Transfer the cheesecake to the refrigerator, covering it with plastic wrap. Chill for at least 4 hours, or ideally overnight.

Carefully remove cheesecake from the springform pan, slice into wedges, and garnish with mint leaves or chocolate sauce before serving.