In a medium bowl, combine the Oreo crumbs and melted butter.
Press crumb mixture into the bottom and up the sides of a 9 inch spring form pan. Place in refrigerator to firm up while preparing filling.
In a large bowl, beat cream cheese, sugar, peppermint extract, and vanilla extract until smooth. Add red food coloring and stir to combine.
Fold in whipped topping and crushed peppermint candy until completely combined.
Spread filling evenly into prepared cookie crust. Cover and refrigerate for at least 4 hours, or overnight.
To make the white chocolate ganache, in a small saucepan, heat heavy cream until boiling.
Remove from heat and stir in white chocolate until completely melted. Set aside to cool.
Pour over chilled cheesecake and lightly spread with a spatula. Top with more crushed peppermint candy, if desired.
Refrigerate until firm.