Preheat your oven to 325 degrees F. Line an 8x8" or 9x9" square baking pan with foil, extending the foil over the edges of the pan. Spray the foil lightly with cooking spray; set aside.
In a large bowl, combine the Oreo cookie crumbs and melted butter, stirring until moistened. Press into the prepared pan in an even layer. Bake for 12 minutes. Remove from oven, but keep oven on.
In the bowl of a stand mixer, cream together the cream cheese and sugar until smooth and creamy, about 2 minutes. Beat in the eggs, one at a time, mixing well after each addition. Beat in the vanilla and peppermint extracts, beating well. Lastly, add in the sour cream and beat well. Fold in the peppermint bark pieces.
Pour the cheesecake filling into the crust and continue baking for 35-40 minutes or until the center is just about set and not sloshing around in the pan; if it jiggles a little, that's okay. Cool completely, then refrigerate for at least 3 hours before cutting into bars.