Preheat your oven to 350°F and line a cupcake tin with liners. Set aside.
In a large bowl, sift together the flour, baking soda, cocoa, and salt. Set aside.
In another bowl, combine both sugars and the butter. Use an electric mixer on medium-high speed to cream until light and fluffy. Add the eggs one at a time, beating for 30 seconds after each addition. Stir in the vanilla extract until well mixed.
Add half of the dry ingredients and ½ cup of milk to the sugar mixture. Mix on low speed until combined. Repeat with the remaining dry ingredients and ½ cup milk, mixing on low until well blended.
Fill the cupcake liners ⅔ full with the batter. Bake for 15-18 minutes, rotating halfway through, until a toothpick inserted into the center comes out clean.
Let the cupcakes cool in the pans on wire racks for 25 minutes, then remove them from the pans and place directly on the racks to cool completely (about one hour).
Oreo Buttercream:
Place the Oreo cookies in a food processor and pulse until they turn into fine crumbs. If you don’t have a processor, add them to a zip-top bag and crush them with a rolling pin until finely ground. Set aside. Sift the confectioners sugar to remove any lumps.
In a large bowl, beat the softened butter using a stand mixer fitted with the paddle attachment (or a hand mixer) on medium-high speed for about 4 minutes, until light and fluffy. Scrape down the sides of the bowl, then continue mixing for another 1–2 minutes.
Add the confectioners sugar, vanilla extract, and milk in two additions. Mix on low speed until combined after each addition, then increase the speed slightly and beat until smooth and creamy. Scrape down the bowl as needed.
Fold in the crushed Oreo crumbs and mix just until evenly incorporated.
Transfer the buttercream to a piping bag fitted with your desired tip. Pipe onto cupcakes and finish by topping each with an Oreo cookie.