Preheat oven to 350°F. Spray a 12-cup muffin pan with nonstick cooking spray.
Take a single piece of cookie dough and flatten it slightly with the palm of your hand. Place an Oreo on top, then flatten another piece of cookie dough around the Oreo forming a ball and completely enclosing the Oreo. Place cookie dough ball into the muffin cup and repeat.
Bake the cookie cups for approximately 20-25 minutes or until golden brown and edges are set. Cool in pan for at least 15 minutes and then run a knife around the edges to help you easily remove it from the pan.
Pipe canned frosting onto the cupcakes. Or make your own frosting: beat butter until creamy with a hand mixer. Slowly mix in powdered sugar, one cup at a time, until it's crumbly, then add vanilla, salt, and 2 tablespoons heavy whipping cream. Beat until smooth and fluffy, adding more cream as needed for consistency. Frost the cupcake cookies with the frosting.
Store loosely covered for up to 3 days.