Place an ungreased 9-inch springform pan on a double layer of heavy-duty foil (about 18 inches square). Securely wrap the foil around the pan. Preheat oven to 350°F.
In a small bowl, combine the graham cracker crumbs with the melted butter. Press the mixture evenly over the bottom of the pan and about 1 inch up the sides of the pan. Place on a baking sheet. Bake at 350°F for 5 minutes. Cool on a wire rack.
Reduce the heat to 325°F. In a large bowl, beat the cream cheese, sugar, vanilla, and peppermint until smooth. Add eggs and beat on low speed just until combined. Fold in crushed peppermint candies. Pour into crust. Place in a larger baking pan. Add 1 inch of hot water to the larger pan. Bake at 325°F for 1 1/2 hours or until center is just set and the top appears dull.
In a small bowl, combine sour cream and sugar until smooth. Spoon over the hot cheesecake and spread to cover. Bake for 5 minutes longer or until the topping is just set.
Remove springform pan from water bath. Cool the cheesecake on a wire rack for 10 minutes. Carefully run a knife around edge of pan to loosen. Cool for 1 hour longer. Refrigerate overnight. Remove sides of pan. Garnish with holiday candies.