Preheat oven to 350 degrees F.
Finely crush (or grind) 25 Oreo cookies, using a food processor or blender.
In a bowl, whisk together the Oreo crumbs, flour, cocoa, baking soda, salt, baking powder, and cream of tartar.
In another large bowl (or stand mixer) cream together the butter and sugars.
Add egg and oil to butter and sugars and mix until smooth.
Gradually add dry ingredients to wet ingredients, mixing until combined. Dough will be stiff.
Scoop out dough onto lined cookie sheet using 1.5 tablespoon cookie dough scoop. Use the bottom of a cup or small bowl to gently flatten the tops of the cookie dough balls.
Bake cookies for approximately 9 minutes. Tops will be puffed and barely cracked and edges will feel slightly dry, but middles will still be quite soft. Cool cookies completely before frosting.
To make frosting, cream together butter and cream cheese. Add powdered sugar, vanilla and milk and beat well until combined and fluffy.
Crush 6 more Oreos (these don't need to be finely crushed, so you can put them in a bag and crush them with a rolling pin). Stir about half of the crushed Oreos into the frosting - don't put too many Oreos in the frosting or it will begin to look gray.
Frost the cookies and sprinkle with the remaining Oreo crumbs.