Preheat the oven to 325°F (163°C). Line the bottom of a 9-inch springform pan with parchment paper.
Combine Oreo crumbs and melted butter. Press mixture firmly into the bottom of the pan. Bake for 10 minutes and let cool.
In a large bowl, beat cream cheese until smooth. Add sugar and vanilla, mixing until combined.
Add eggs one at a time, beating on low after each just until blended.
Divide batter evenly into three bowls. Tint one red, one green, and leave one plain.
Pour red batter over crust and spread evenly. Carefully layer the plain batter, then the green batter on top.
Bake for 50–60 minutes or until the center is almost set. Turn off the oven and leave the cheesecake inside for 1 hour.
Remove and cool completely, then chill at least 4 hours or overnight.
Before serving, whip heavy cream and powdered sugar to stiff peaks. Pipe or spread over cheesecake and garnish with sprinkles.