Line two sheet pans with parchment. Slide one pan into the freezer to pre-chill while you work.
Combine the powdered sugar and the finely chopped Andes peppermint chips in a large zip-top bag (2-gallon size works best). Seal and shake to mix; set aside.
Spread the cereal over the remaining lined sheet pan and warm in a 225°F oven for 6 minutes to crisp it slightly. Let it cool on the pan for 2 minutes so it’s warm but not hot.
Set a medium heatproof bowl over a small pot of barely simmering water (the bowl should not touch the water). Add butter, white chocolate chips, and semi-sweet chocolate chips. Stir constantly until smooth and glossy, 3 to 4 minutes. Remove from heat and stir in peppermint extract, vanilla, and salt. Let the mixture stand 1 minute to thicken slightly.
Transfer the warm cereal to an extra-large bowl. Drizzle half of the melted chocolate over the cereal and fold gently with two spatulas until most pieces are lightly coated. Add the remaining chocolate and fold again until evenly covered.
Work in two batches: Scoop half of the coated cereal into the prepared bag. Seal with some air inside and shake vigorously until the pieces look snowy and separate easily. Spread onto the chilled sheet pan. Repeat with the remaining cereal and sugar mix.
Chill the pans for 10 minutes, or let set at cool room temperature for about 20 minutes. Break apart any larger clusters and serve.
Store in an airtight container at room temperature up to 3 days or refrigerate up to 1 week.