Place some wax or parchment paper onto a large cookie sheet and set aside.
Using a double boiler or a pan on VERY low heat, heat the dark chocolate chips with 1/4 tsp of coconut oil until smooth and JUST melted. DO NOT OVERHEAT.
Pour the dark chocolate onto the prepared jelly roll pan making a large rectangle in the middle of the pan. The larger the rectangle, the thinner the bark. For thicker bark, make a smaller rectangle.
Place pan into the refrigerator to set, about 10 minutes.
In a microwave safe bowl, add 1/3 cup of white chocolate chips and 1/4 cup of peppermint baking chips. Set aside. Using the same method as the dark chocolate, melt the remaining white chocolate chips with 1/4 tsp of coconut oil. Once the white chocolate is melted it is optional to add 1/2 teaspoon of peppermint extract.
Melt the white chocolate and peppermint chips in the microwave on 50% power stirring every 30 seconds until melted.
Remove the dark chocolate pan from the refrigerator and spread the melted white chocolate on top covering as close to the edge as possible.
Drizzle the melted white chocolate peppermint chips mixture up and down on white chocolate.
Using a knife, gently swirl side to side creating a beautiful design and sprinkle candy cane pieces on top. You want to do this quickly before the the chocolate sets.
Allow the bark to cool completely on the counter or refrigerator. Break apart by hand or a knife. Store in an airtight container.