1. Preheat oven to 325 degrees F and line baking sheets with silicone baking mat or parchment paper.
2. Whisk together flour, salt, baking powder and cocoa, and set aside. Beat the butter on medium-high until light and add sugars, creaming well. Add the vanilla and beat until smooth. Add the flour mixture in 2 batches, alternately with the milk in one batch, mixing well. Using a spatula, mix in the white chocolate. Chill dough for 15 minutes.
3. Scoop the dough onto a parchment- or silpat-lined cookie sheet, press down on them slightly, and bake (see note below). Let the cookies cool completely on the cookie sheet and store in an air-tight container.
Note #1: Shawnda states that she uses a No 12 scoop to drop a well rounded scoop of chilled cookie dough (a little less than 1/2 cup of cookie dough) and bakes for 24 minutes. At this size she gets 8 or 9 cookies with a diameter of 6 inches using the No 12 scoop. If you scoop a more normal sized cookie, she estimates 12-16 minutes in the oven. I used a large cookie scoop from Pampered Chef, which is approximately 3 Tablespoons in size, and I got 13 cookies out of my batch, with 18-20 minutes in the oven seeming to do the trick.
Note #2: Substituting with natural unprocessed cocoa is not recommended. The Oreo-like flavor comes from the richer dutch-processed cocoa. I used Hershey Special Dark blend of dutch-processed and natural because I cannot find pure dutch-processed in these parts for the life of me!