Cream the butter and shortening and vanilla in a large bowl, with a hand mixer or in a stand mixer.
Slowly add the powdered sugar, mixing thoroughly between each addition.
After all of the sugar is mixed in and mixture is thoroughly mixed, add the very cold milk, one tablespoon at a time, combining very well after each addition, until you reach the desired consistency.
Fold in the Oreo cookie crumbs.
Pipe the frosting onto cooled cupcakes- Use a large frosting tip, as the Oreo crumbs can clog smaller tips. Garnish with half an Oreo or a mini Oreo.