Line the bottom and sides of a 9x12 inch rectangle baking pan with parchment paper, smoothing out any creases; set aside.
Place the semi-sweet chocolate into a medium-sized heatproof bowl. Melt in the microwave, in 20 second increments, stirring with a rubber spatula and scraping down the sides after each increment, until chocolate is completely melted and can be stirred completely smooth. Once melted, stir in a 1/4 teaspoon of the peppermint extract. Quickly pour the melted semi-chocolate into the prepared baking pan, spreading with a spatula into a thin smooth layer. Place the baking pan in the refrigerator for 20 minutes; it will not be completely set.
In the meantime, prepare the next chocolate layer. Combine the white chocolate and oil in a medium-sized heatproof bowl and microwave according to the same instructions you followed to melt the semi-sweet chocolate. Once melted, stir in remaining 1/4 teaspoon peppermint extract and whisk smooth.
Sprinkle half of the crushed candy canes and half of the chopped Oreo cookies on top of the semi-chilled chocolate. Then pour all of the white chocolate on top. Carefully spread into a smooth layer. Evenly sprinkle remaining crushed candy canes and Oreo cookies on top of the wet chocolate. Refrigerate the bark until completely hardened, about 1 hour. Once completely set, remove the chocolate from the pan and discard the parchment paper.
Break into pieces large or as small, or use a very sharp knife to cut it into large or small squares. Store bark in the refrigerator and bring to room temperature right before serving.
This recipe will keep, when stored in the refrigerator in an airtight container, for up to 2 weeks.