In a large bowl, whisk together flour, milk powder, baking powder and baking soda.
In a food processor, add 7 cookies and pulse until powder like. If you don’t have a food processor, you can put cookies in a large Ziploc bag and crush with a rolling pin. For the rest of cookies, break them into pea-sized pieces. Keep the powder and cookie pieces separate and set aside.
In a large mixing bowl with an electric mixer fitted with a paddle attachment, beat the butter until smooth. Add both sugars and beat on medium speed for 3 minutes. Scrape down the sides of the bowl. Add salt and vanilla extract. Beat again. Add egg and beat to combine. Add Oreo powder and beat together. Add the dry ingredients and mix until just blended.
Remove the bowl from mixer. Using a wooden spatula, mix in half of the cookie pieces. Try not to break up the cookies too much. Wrap the dough tightly in plastic wrap. Chill in the fridge overnight. Transfer the rest of the cookie pieces to a small Ziploc bag.
The next day, preheat the oven to 350˚F (177˚C). Line a baking sheet with parchment paper.
Scoop out dough and roll into a ball (about 1½-inch diameter). Put the ball on the prepared baking sheet, and space them apart for about 2 inches. Press down the ball slightly, about 1-inch in height. Gently add 2 – 3 pieces of cookie pieces on top. Repeat with the rest of the dough. Keep the balls in the fridge until ready to bake.
Bake in the oven for 13 – 14 minutes. The bottom of the cookie should be nicely golden brown, but the top and edges remain the same color. Transfer the baking sheet to counter and let the cookies rest on the sheets for at least 5 minutes. Transfer the cookies to racks and cool. Repeat with the rest of the cookie dough.