In a bowl, stir together the cream and milk. Add the sugar and whisk until the sugar is dissolved, 3 to 4 minutes. Test for graininess by tasting a small amount of the liquid; it should feel smooth on the tongue and there should be no sugar visible on the bottom of the bowl when it is stirred or spooned out. Continue whisking, if necessary, to ensure that the texture of the finished ice cream will be smooth.
Place a piece of plastic wrap directly onto the surface and on top of the bowl. Refrigerate for at least 3 hours or up to 24 hours.
Prepare an ice cream maker with at least a 1-quart capacity according to the manufacturer's instructions. Remove the plastic wrap from the cream mixture and bowl. Pour the well-chilled cream mixture into the mixing container of the ice cream maker and churn according to the manufacturer's instructions.
While the ice cream is churning, crush Oreos in a food processor or food chopper until you have 2 cups of crushed Oreos. Add crushed Oreos to ice cream mixture when ice cream is almost done and allow to churn until the Oreos are well-distributed throughout the ice cream mixture. When the ice cream is the thickness you desire, you can chill it 4-6 hours or eat it right away if you like a soft-serve consistency.
The timing will depend on the type of machine and the temperature of the cream mixture.