Melt 4 oz. high quality white chocolate broken into pieces with ½ vegetable oil, stir in ⅛ teaspoon peppermint extract and spread onto parchment paper lined tray or baking sheet. Place in the freezer for 15-20 minutes.
Line the bottom of 9 inch springform pan with parchment paper and grease the sides of the pan, then place springform pan on a double thickness of heavy-duty foil and securely wrap foil around pan to make sure no water gets in during the baking.
Combine finely crushed Oreo crumbs and melted butter, then press the mixture evenly into bottom of 9 inch springform pan. Set in the fridge to firm the crust while making the filling.
Preheat oven to 350 degrees.
In a large bowl, beat cream cheese and sugar until smooth. Beat in the sour cream, flour, salt and extracts. Add eggs one at a time and beat on low speed just until combined.
Toss chopped frozen peppermint bark with 1 tablespoon flour, then gently stir the pieces into the cheesecake filling and pour over the Oreo crust, smooth the top and place springform pan in a large roasting pan and add 1 inch of hot water to larger pan.
Reduce temperature to 325 degrees and bake the cake for 70-90 minutes (until center is just set and top appears dull).Turn off the oven and leave the cheesecake in the oven for additional 30 minutes.
Remove springform pan from water bath. Cool on a wire rack 10 minutes. Carefully run a knife around edge of pan to loosen; cool 1 hour longer, then refrigerate for at least 4 hours or overnight.