Make the Cake
Preheat the oven to 325 degrees F.
Thoroughly grease and flour a 10-inch Bundt pan. Be sure to coat all the crevices.
In a large mixing bowl, beat the cream cheese until smooth and creamy.
Add the sour cream, melted butter, milk, and vanilla extract. Add the eggs one at a time. Mix until well combined.
Add the cake mix and mix on low speed just until incorporated. Do not overmix.
Fold in the chopped Oreo cookies with a spatula.
Spoon the batter into the prepared Bundt pan and smooth the top.
Bake for 55-65 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Cool the cake in the pan for 15 minutes.
Invert onto a wire rack and cool completely before frosting.
Make the Frosting
Beat the cream cheese and butter together until light and fluffy, scraping down the sides.
Gradually add the powdered sugar, mixing until smooth. Add the vanilla extract.
Add the cream one tablespoon at a time until the frosting reaches piping consistency.
Decorate
Transfer the frosting to a piping bag or large zip-top bag. Pipe thick ribbons of frosting from the top edge of the cake down the sides, just like a bakery-style Bundt cake.
Sprinkle additional chopped Oreo cookies over the frosting if desired.