Measure the cereal into a large mixing bowl and set aside. Prepare a large baking sheet lined with parchment paper.
Combine semi-sweet chocolate chips, peanut butter, and butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until completely smooth and melted (about 90 seconds total).
Stir the peppermint extract into the melted chocolate mixture until evenly distributed. Pour the chocolate mixture over the cereal and gently fold with a spatula until every piece is coated.
Transfer the coated cereal to a gallon-sized zip-top bag. Add the powdered sugar, seal the bag, and shake vigorously for 1-2 minutes until the cereal is evenly covered in a white coating.
Spread the coated mixture onto the prepared baking sheet in a single layer. Let it cool for 10 minutes at room temperature.
While the mix cools, melt the white chocolate chips in the microwave in 20-second intervals, stirring until smooth. Drizzle the melted white chocolate over the cooled puppy chow using a spoon or fork.
Immediately sprinkle the crushed candy canes and mini chocolate chips over the white chocolate drizzle before it sets. Let it sit for 15 minutes until the white chocolate hardens completely.
Break apart any large clusters and transfer to an airtight container for storage. The mix is ready to serve immediately or can be stored for up to two weeks.
