Divide the Chex cereal into two separate bowls measuring 2½ cups each.
In a food processor pulse the Oreos until fine.
In 2 separate gallon-size Ziplock bags, add ½ cup powdered sugar into each bag. Divide the crushed Oreos into each bag and set aside. (It was about 1/2 cup of crushed oreos.)
Melt the white chocolate and milk chocolate in separate microwave-safe bowls. Add ½ teaspoon shortening in each bowl, stirring every 30 seconds until melted.
Once melted, stir in the chocolate into the separate bowls with Chex cereal until the Chex are coated well with the chocolate.
Add the white chocolate and milk chocolate separately to each gallon-sized bag of powdered sugar/cookie mixture and shake until they are coated. Then crush a few extra Oreos to toss with the mixture and enjoy!