Grease the inside of a large mixing bowl with butter then pour in the box of cereal, the chopped cookies, tossing lightly to combine.
Melt the butter in a large saucepan on low heat.
Add the bag of marshmallows. Stir, melting the marshmallows, until they have dissolved into a smooth mixture. Remove from the heat and stir in the vanilla extract.
Pour the marshmallow mixture over the cereal and cookies and gently stir to coat evenly.
Turn out the cereal mixture into the prepared pan. Butter your hands, then firmly press the mixture into an even layer. Cover with plastic wrap and let sit until it sets, about an hour.
Slice into squares and serve.
Store in a closed container for up to 5 days at room temperature.