Preheat the oven to 325°F (160°C). Grease a 9-inch springform pan.

In a mixing bowl, combine graham cracker crumbs and melted butter. Press the mixture firmly into the bottom of the prepared springform pan to form the crust.

In a large bowl, beat the cream cheese and granulated sugar together until smooth and creamy. Add the vanilla extract and mix well.

Add the eggs one at a time, mixing well after each addition. Then, stir in the sour cream and heavy cream until fully combined.

Divide the cheesecake batter into two bowls. In one bowl, add the green food coloring and mix until you reach your desired color. Leave the other bowl plain.

Pour alternating spoonfuls of the green and plain batter into the center of the crust, creating a swirl effect. Use a knife or skewer to gently swirl the two colors together for a marbled look.

Drizzle the chocolate syrup on top and use a knife to swirl it into the cheesecake.

Bake in the preheated oven for 50-60 minutes, or until the edges are set but the center is still slightly jiggly. Turn off the oven and leave the cheesecake inside for an additional hour.

Remove from the oven and let it cool to room temperature. Refrigerate for at least 4 hours, or overnight, before serving.