Preheat oven to 350 degrees F. and line large baking sheet with parchment paper.
Cream butters and sugars in large bowl or stand mixer. Add eggs and vanilla beating until well combined. Stir in flour, cereal, baking soda, salt and chocolate chips. Using a medium-large cookie scoop at least 2 tablespoons, scoop dough onto prepared baking sheet at least 1 inch apart from each other. Bake for 13-15 minutes until golden edges and baked through. Let cool on cookie sheet for 10 minutes before transferring.
If making cookie sandwiches, prepare frosting. In a medium mixing bowl, cream peanut butter and butter until smooth. Stir in powdered sugar until thick and spreadable. Spoon frosting on inside of one cookie and top with a second cookie. Place Reese’s Puff Cereal on outside of frosting if desired.