Preheat oven to 350 degrees F. Line muffin tins with paper liners. Set aside.
In the bowl of a stand mixer, stir together sugar, flour, cocoa, baking powder, baking soda and salt.
Add eggs, milk, oil and vanilla. Beat on medium speed for one minute or until batter is smooth. Slowly pour in boiling water and mix until batter is smooth. Don't over mix.
Place an Oreo cookie at the bottom of each paper liner. Fill liners 1/2 full with batter, covering the cookie. Bake cupcakes for 18-22 minutes or until a toothpick inserted in the center comes out clean. Remove from oven and cool completely on wire rack before frosting.
While the cupcakes are cooling, make the frosting. Using a stand mixer, beat the butter until creamy. With the mixer on low, add 1 cup of powdered sugar at a time until all of the powdered sugar is added. Beat in the vanilla and milk. Mix until smooth. Beat in the chopped Oreo cookies. Mix until combined.
Place the frosting in a pastry bag and frost. Top with mini Oreo cookie, if desired. Serve!