Start by lining a 9×13 pan with parchment paper and lightly misting it with nonstick cooking spray. Set it aside.
In a large pot, melt the butter. Keep stirring until the butter just begins to brown. Watch for it to foam up twice and then give off a nutty aroma. Remove it from heat immediately to prevent burning. Stir in the two teaspoons of vanilla extract, but be careful as the hot mixture will bubble up and steam.
Add in half of your marshmallows and mix until almost completely melted before adding the rest. Stir until all the marshmallows are mostly melted. Then, add in the Rice Krispies, 2 cups at a time, and lightly stir until combined.
Continue adding the Rice Krispies and Cookie Crisp cereal until everything is evenly combined. Finally, mix in the chopped Chips Ahoy Cookies until just combined. Pour the mixture into the prepared pan and gently press it down. Wet your hands lightly to prevent sticking. Allow it to set and cool for 30 minutes.