Combine 2 1/4 cups cookie crumbs and butter; stir well. Firmly press onto bottom and 2" up sides of a 9" springform pan. Bake at 350° for 8 minutes. Remove to a wire rack; let cool. Reduce oven temperature to 325°.
Beat cream cheese at medium speed of an electric mixer until creamy; gradually add sugar, beating well. Add 1/2 cup whipping cream, flour, and vanilla; beat well. Add eggs, one at a time, beating after each addition. Stir in 1 cup chopped cookies and 1/3 cup crushed peppermint candies. Pour batter into prepared crust.
Bake at 325° for 1 hour or until almost set. Remove to a wire rack; let cool completely. Cover and chill at least 8 hours. Remove sides of springform pan.
Bring water to a boil in bottom of a double boiler; remove from heat. Combine white chocolate and 1/3 cup whipping cream in top of double boiler; place over hot water. Heat until chocolate is melted and smooth, stirring constantly with a rubber spatula. Let mixture cool slightly (3 to 5 minutes).
Spread white chocolate mixture over top and sides of cheesecake. Garnish with candy canes.