Preheat the oven to 350 and line a couple of large baking sheets with parchment.  Using your electric mixer, beat together the butter and both sugars for a couple of minutes until well mixed and fluffy, scraping down the sides of the bowl as needed.  Beat in the eggs, one at a time, until combined, then scrape down the bowl and beat in the vanilla.

Stir in the flour, malted milk powder, baking soda and salt and once there is no trace of dry ingredients (I found the dough really sticky, so next time I’m going to try adding another 1/4 to 1/2 cup of flour), then fold in the Oreos and both kinds of chocolate.

Roll into large (2 tablespoon-sized) balls and place them a good 3 inches apart on your prepared baking sheets and bake for 10 to 12 minutes, depending on how chewy or crunchy you’d like them.  Allow the cookies to rest for several minutes before transferring them to a rack to cool.