Use parchment paper to line a 9x13 baking sheet that has sides.
In a microwave safe bowl, heat dark chocolate on 50% power, in 30 second increments. After each 30 second increment, stir will. Continue heating/stirring until smooth. Use a spatula to spread dark chocolate evenly over parchment paper. It will be a very thin layer but will be able to cover the entire lined bottom of the pan. Place in refrigerator for at least 10 minutes.
Next, heat semi-sweet chocolate in the same manor; 50% power in 30 second increment, stirring after each increment, until smooth. Spread the smooth chocolate over the dark chocolate in the pan. Immediately sprinkle crushed Oreos even over the chocolate and gentle press them down. Return baking sheet to refrigerator for at least 10 more minutes.
Heat peppermint white chocolate in same major as the dark and semi-sweet chocolates. Once smooth, either drizzle the chocolate over the Oreo layer, or use a spatula to spread it over. Immediately top with the crushed candy cane. Gently press down candy cane bits.
Return pan to refrigerator at least 20 minutes. After this, break into small pieces, about 2"x2", and store in airtight container or bag.