In a microwave-safe bowl, combine the semi-sweet chocolate chips and crushed peppermint candies. Microwave for 1 minute, then stir. Continue melting in 30-second intervals, stirring after each, until the mixture is smooth and fully melted (this typically takes 1.5 to 2 minutes total).

Place the Rice Chex cereal in a large mixing bowl. Pour the melted chocolate-peppermint mixture over the cereal. Gently fold with a large rubber spatula or wooden spoon until all the cereal is evenly coated.

In a large (gallon-sized) Ziploc bag, add the powdered sugar. Carefully spoon the chocolate-coated cereal into the bag. Seal the bag, ensuring there's plenty of air inside, and shake vigorously until the cereal is completely coated with powdered sugar.

Pour the puppy chow onto a large piece of wax paper or parchment paper to cool and set, about 15-20 minutes. Once set, add the optional crushed candy canes and peppermint M&M's, if using, and gently mix. Store in an airtight container at room temperature.