Grease or butter a 9x13 pan. Place Oreos in food processor and pulse into ground (you may have to work in batches). Pour Oreos into a large bowl. In another large microwave-safe bowl, melt marshmallows and butter for 60 seconds. Stir. Repeat until mixture is melted and mixed together. Pour over Oreos. Stir, using a wooden spoon, until mixed well. Mixture will become thick and hard to stir. Keep mixing until all the crumbs are incorporated. Pour into prepared pan and press to spread evenly. I find it helps to spray my fingers, or a wooden spoon with cooking spray to press the mixture without sticking. Set aside. Place white chocolate chips in a zip-loc baggie. Place in microwave for 20 seconds. Take out and knead to mix. Repeat until chocolate is melted. Cut off a small piece of the corner of the bag and drizzle bars with chocolate. I usually place them in the fridge to hurry the process (but if you leave them too long, you will have to let them sit out to soften before cutting). Once chocolate has set, cut into bars and enjoy.
If you want to make a smaller batch, use a 8x8 pan and only half of the ingredients.