Combine white chocolate and 3 tbsp of milk (reserving the final one) into an oversized microwaveable mug. Microwave for about 30 seconds. Stir with a fork until chocolate is melted. Chocolate should melt, but it may not be completely smooth. Microwave for another 20 seconds and stir again. Chocolate should be thickened and completely melted and smooth. Add in flour and baking powder. Stir with a small whisk until batter is smooth. It will be quite thick. Add in the additional 1 tbsp milk and stir again. This will loosen the batter.

Add in two Oreos. Using fork, smash Oreos into mug. Continue to mash oreos into the batter until only small chunks remain. Microwave for approximately 1 minute. Top of cake should be dry. You can pry edges of cake to check inside of cake with a fork, to make sure it is done cooking. Let cake cool completely in mug so that it sets before eating (about 20 minutes).