Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, melted butter, and granulated sugar. Mix until well combined. Press this mixture into the bottom of a 9-inch springform pan. Bake for about 10 minutes, until golden.

In a large mixing bowl, beat together cream cheese and sour cream until smooth. Gradually add sugar, mix until dissolved, then add eggs one at a time, blending after each. Add vanilla extract.

Divide the filling in half; keep one part plain. Mix green food coloring into the other half. Alternate spoonfuls of both fillings in the pan and gently swirl them together.

Bake the cheesecake for 55-60 minutes until the center is set with a slight jiggle. Turn off the oven, crack the door, and let it cool inside for 30 minutes.

After cooling, refrigerate for at least 4 hours or preferably overnight, covered to retain moisture.

Remove from springform pan, garnish with fresh mint leaves or chocolate shavings, slice, and serve on a platter.