Preheat oven to 325°F (163°C). Line and grease a 9-inch springform pan.
Crush Oreos until fine. Mix with melted butter until combined. Press into bottom of pan and chill.
Beat cream cheese until smooth. Add sugar and mix well.
Add sour cream, vanilla, buttermilk, and vinegar. Mix to combine.
Add green gel food coloring drop by drop to achieve desired color.
Beat in eggs one at a time on low speed, mixing gently.
Pour batter over crust. Tap to release air bubbles and smooth the top.
Wrap pan base in foil, place in roasting pan filled with 1 inch hot water.
Bake 60–70 minutes, until edges set and center jiggles slightly.
Turn off oven, crack door, let cheesecake cool in oven for 1 hour.
Remove from oven, cool to room temperature, then refrigerate at least 6 hours or overnight.
Decorate with whipped cream and crushed Oreos before serving.