Add the Rice Chex cereal to a large mixing bowl and set aside.
Place the semisweet chocolate chips, peanut butter, and butter in a microwave-safe bowl.
Microwave in 20 to 30 second intervals, stirring well after each interval, until the mixture is smooth and completely melted.
Stir the vanilla extract and peppermint extract into the melted chocolate mixture.
Pour the warm chocolate mixture over the cereal. Gently fold with a rubber spatula until the cereal is evenly coated, taking care not to crush the pieces.
Transfer the chocolate-coated cereal to a large resealable bag or container. Add the powdered sugar, seal, and gently shake until the cereal is covered.
Spread the puppy chow onto a parchment-lined baking sheet or clean surface.
Sprinkle the crushed peppermint candies over the mixture and gently toss to distribute them evenly.
Let the puppy chow sit uncovered for 20 to 30 minutes, or until the chocolate coating has completely set.
Break apart any large clusters and transfer the finished puppy chow to an airtight container.
