Mix all ingredients except the Oreo cookies together in a freezer safe container. Freeze for 2-3 hours or until the mixture is partially frozen and has a thick consistency.
Stir in ½ cup or more of the crushed Oreo cookies until evenly distributed. If the Oreos sink to the bottom, the ice cream needs to freeze longer. Continue freezing at least 2-3 hours until fully frozen.
Top with additional Oreo cookie crumbles and serve.