Preheat oven to 350 degrees F (175 degrees C). Wrap the bottom of a springform pan with aluminum foil.
Mix 25 crushed cookies with butter in a large bowl. Press into the bottom of a springform pan to form crust.
Beat cream cheese, sugar, and vanilla extract together in a bowl with an electric mixer until smooth. Beat in eggs one at a time, mixing well between each addition. Fold in 10 crushed cookies and peppermint extract.
Spread cream cheese mixture over crust. Set springform pan in a deep baking dish. Pour enough water into the baking dish to come halfway up the sides of the pan.
Bake in the preheated oven until center of the cheesecake is set, 45 to 60 minutes. Turn off oven and open door slightly, leaving cheesecake inside to cool, about 1 hour. Refrigerate until firm, about 4 hours.