Mini Oreos or reserved halves from the cupcake bottoms, for garnish
Make the Cupcakes
Preheat oven to 350 F. Line two cupcake pans with paper liners and set aside.
With a paring knife (or just twist if you're brave!), remove one side of 24 of the Oreos, leaving the filling intact. Place an Oreo half with the filling filling-side-up in each of the cupcake liners.
Roughly chop the remaining whole Oreos and set aside.
Sift flour, cocoa powder, baking soda, baking powder and salt into a large bowl. Add sugar and whisk to combine.
In another large bowl, mix together the vegetable oil, eggs, vanilla, sour cream and coffee until incorporated. Pour into the bowl with the flour mixture and stir until well-mixed and smooth. Gently fold in the chopped Oreos.
Divide batter evenly among prepared pans, filling each ⅔-3/4 full. Bake 18-20 minutes, until a toothpick inserted in the center comes out clean.
Make the Frosting
In a large bowl or the bowl of a stand mixer, beat butter and shortening until fluffy. Add vanilla and mix to incorporate.
Sift in powdered sugar, a few tablespoons at a time, mixing well between each addition.
Pipe onto cooled cupcakes and garnish with an Oreo half, a mini Oreo, or Oreo crumbs