Place the heavy cream and whole milk in a small pot over low heat. Place the sugar and xanthan gum in a small bowl and stir to combine (this helps the xanthan gum not clump when added to the mixture). Pour the sugar mixture into the hot cream and milk and whisk to combine. Add the corn syrup and stir. Carefully pour the mixture into a large bowl.
While the mixture is still hot, add the Oreos. Stir as the Oreos break down into the mixture. Use an immersion blender to completely break down the Oreos (if you don’t have an immersion blender, use the back of a spoon to break up the Oreos). Pour the mixture through a strainer to remove any remaining clumps. Cover the bowl and transfer to the fridge to cool completely.
While the ice cream base cools, make the Oreo crumble. Preheat the oven to 350 F. Add the remaining Oreos to a food processor and pulse until fine crumbs. Add the butter and salt and pulse until combined. Transfer the mixture to a baking sheet and spread it out evenly. Transfer to the oven and bake for 10 minutes. Set aside to cool completely.
When the ice cream base is cold, transfer to your ice cream machine and churn for 15-20 minutes. You can either add the Oreo crumble in the last 5 minutes of churning, or layer it with the ice cream when transferring to a container. Once in the container, transfer to the freezer to set up, at least 2 hours (you can eat it right after churning, but it is very soft!).